Method and device for recording sequence information on biological compounds

ABSTRACT

A method and device for recording sequence information on biological compounds such as nucleotides and amino acids in as small amounts of data as possible are provided. The text data representing the sequence of a series of nucleotides constituting the DNA of the standard sample E is converted into binary data using a conversion table, and the binary data is divided into plural m-bit partial data (A(i,j)) arranged in plural columns and rows (m≧16). Then a first set of parities (B 1 ( i )˜B 3 ( i )) are computed by applying an operation of Galois field GF(2 m ) to the partial data (A(i,j)) of each column and a second set of parities (C 1 ( j )˜C 3 ( j )) are computed by applying an operation of Galois field GF(2 m ) to the partial data (A(i,j)) of each row. The sequence of the nucleotides is represented approximately by the parity information.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part of PCT Application No.PCT/JP02/03801 filed Apr. 17, 2002, which application has not beenpublished in English under PCT Article 21(2), and both the presentapplication and the preceding PCT application claim priority under 35U.S.C. § 119 to Japanese patent application JP2001-120335 filed Apr. 18,2001, and Japanese patent application JP2001-368002 filed Nov. 30, 2001.Moreover, all the disclosures including descriptions, claims, drawings,and abstracts of the Japanese patent application JP2001-120335 filedApr. 18, 2001, the Japanese patent application JP2001-368002 filed Nov.30, 2001, and U.S. application Ser. No. 10/272,107 filed Oct. 16, 2002are incorporated herein by reference.

TECHNICAL FIELD

The invention relates to a method and device for recording sequenceinformation on biological compounds such as a set of nucleotidesconstituting at least part of nucleic acids, e.g. DNA (deoxyribonucleicacid), RNA (ribonucleic acid), and genes, and a set of amino acidsconstituting at least part of proteins.

The invention further relates to a method for supplying sequenceinformation suitable for a business model to supply the sequenceinformation and to a computer-readable medium in which the sequenceinformation is recorded.

BACKGROUND ART

The sequences of nucleotides (or bases) in pairs of polymer strandsconstituting the DNA molecules of humans and other organisms (animals,plants, microorganisms, etc.) are being deciphered worldwide. In orderto record the deciphered nucleotide sequences, four kinds of nucleotideswhich constitute DNA are expressed in four different one-byte(eight-bit) text data by allocating the character A, G, C, or T for thenucleotide including adenine, guanine, cytosine, or thymine respectivelyas the nitrogenous base. Consequently, sequence information on DNA whichconsists of two polymer strands with each strand comprising n (n is aninteger) nucleotides is represented in n-byte text data by expressingeach nucleotide of one strand one by one as the corresponding characterselected from the four characters A, G, C, and T (or a, g, c, and t).Similarly, the sequence of n nucleotides constituting an RNA molecule isrecorded in n-byte text data by allocating the character A, G, C, or U(or a, g, c, or u) for the nucleotide including adenine, guanine,cytosine, or uracil respectively.

In the case of humans, since each chain of the DNA molecules in thefirst or largest chromosome and in the 22nd or smallest one is asequence of nearly 250,000,000 and 50,000,000 nucleotides respectively,the nucleotide sequence of the DNA in each chromosome can be expressedin about 250-50 MB text data. In addition, since the human genome (allDNA information) is expressed as the sequence of nearly 3,000,000,000nucleotides, it is recorded in about 3 GB text data. For practical uses,the original text data may be recorded or transmitted as a compressedfile of about half the size of the original data by applying theconventional file compression techniques.

Following the decipherment of nucleotide sequences of DNA, the functionsof the proteins synthesized according to the genes in DNA are widelyresearched. In these researches, the sequence of a protein moleculewhich consists of n amino acids is represented by n-byte text data sinceeach of 20 kinds of amino acids constituting protein molecules isexpressed as the text data of three characters (for example, Ala, Cys,Glu, etc.) in three-Letter Code or one character (for example, A, C, E,etc.) in one-Letter Code. As ordinary proteins consist of the sequenceof nearly 20 to 1000 amino acids, each of the sequences of thoseproteins may be recorded in about 1 KB text data, at the most. Moreover,it is estimated that there are nearly 30,000 human genes in total andthere may be nearly 100,000 kinds of protein molecules includingtheoretical ones.

As described above, in order to record the human genome in the form oftext data, about 3 GB of memory is necessary. Even if the conventionalfile compression techniques are employed, nearly 1 GB of memory may beneeded. Recently, DNA sequences of living organisms other than humanssuch as colon bacilli and various viruses are also disclosed to thepublic. If these DNA sequences are collected in text data, we may needseveral hundred MB of memory for each of those organisms. Such is thecase in recording sequence information on RNA.

Thus, when information on DNA sequences of humans or other organisms isrecorded in the form of text files or the conventional compressed files,the recording medium with huge memory capacity such as a DVD-ROM diskcapable of recording nearly 5 GB data is necessary. There isadditionally an inconvenience that both the time needed for readingsequence information from the recording medium and the time needed forprocessing sequence information are long.

Moreover, since the transmission rate of the current generalcommunications network is about 5 Mbps, when we transmit information onDNA sequences of the size of, for example, 1 GB via the communicationsnetwork, the transmission time will be around thirty minutes. Especiallyrecently the digital cellular phone system is being widespread as acommunications medium. It may however be difficult to use it to transmitat least the DNA sequence information of humans since the transmissionrate of the present cellular phone system is as low as nearly 1 Mbps.

There is also a problem of how to assure that the nucleotide sequences,which are assumed to be equal and held by two or more researchers as astandard sequence, are really equal. This happens, for example, whengenes in the DNA of a certain microorganism are studied by theresearchers. That is, it is not necessarily easy for two or moreresearchers to mutually verify in a short time that their text dataexpressing the nucleotide sequence of the DNA are completely equal wheneach of their text data has several MB data (data for several millioncharacters).

In this connection, as a use of information on DNA sequences of humansor other organisms, we can think of a task to search the differencebetween a standard DNA sequence and a sample DNA sequence. Such a taskwill be needed when the SNP (Single Nucleotide Polymorphism) issearched. However, there is an inconvenience that a relatively long timeis needed to compare the two text data and search the difference betweenthem when both text data represent the huge nucleotide sequence of DNA.

Furthermore, a new business has started in which several suppliers offermany pieces of information on DNA sequences to users such as researchersof the pharmaceutical companies. In the business it is preferable forthe suppliers to avoid offering overlapping information to the users. Itis thus convenient for the users to be able to check easily whether thenucleotide sequences of DNA offered by the plural suppliers are equal ornot without disclosing the entire information on the nucleotidesequences to the public. In addition, when the suppliers offer the usersthe DNA information through, for example, a communications network, abusiness model is needed in which necessary information can betransmitted to the users in as less data as possible so as to shortenthe transmission time. Moreover, it is preferable that the users caneasily check whether the offered DNA information contains transmissionerrors, etc. The above-mentioned problems are included similarly intreating information on nucleotide sequences of RNA.

In addition, the amino acid sequence of a protein is recorded by thetext data of about 1 KB at the most and there are about 100,000 kinds ofproteins including theoretical ones. Thus, if we express sequenceinformation on all kinds of proteins in the form of text data, we willhave a large amount of data. Accordingly, it is preferable to record thesequence of each protein in as less data as possible and we need asystem by which we can easily verify whether two pieces of sequenceinformation on proteins are equal.

It is therefore an object of the present invention to provide a methodand device for recording approximate small amounts of data of sequenceinformation on biological compounds such as a set of nucleotides ofnucleic acids or a set of amino acids of proteins.

It is a second object of the invention to provide a method and devicefor detecting the difference between two pieces of sequence informationon biological compounds by a small amount of data and, if necessary,recovering the difference.

It is a third object of the invention to provide a business model (or amethod for supplying information) for making a user easily verifywhether the user's data and the supplier's original data are equal anddetect the difference between them using a small amount of data whensupplying sequence information on biological compounds such as a set ofnucleotides or a set of amino acids to the user.

It is a fourth object of the invention to provide a computer-readablemedium in which approximate information on sequences of biologicalcompounds is recorded with a small amount of data.

DISCLOSURE OF INVENTION

According to one aspect of the invention, a first method for recordingsequence information on biological compounds comprises the followingsteps:

-   -   dividing the text data representing the sequence of the        biological compounds or the numerical data obtained by        converting the text data based on a conversion rule into plural        m-bit partial data (A(i,j)) arranged in plural columns in the        arranged direction corresponding to the direction along which        the biological compounds are placed and in plural rows in the        non-arranged direction which crosses the arranged direction,        where m is an integer larger than or equal to 16;    -   computing a first set of parity information (B1(i), B2(i),        B3(i)) by applying a first operation of Galois field GF(2^(m))        along the non-arranged direction to a set of the partial data of        each column;    -   computing a second set of parity information (C1(j), C2(j),        C3(j)) by applying a second operation of Galois field GF(2^(m))        along the arranged direction to a set of the partial data of        each row; and    -   representing the sequence information on the biological        compounds by the first and second sets of parity information.

In this aspect of the invention, the biological compounds are supposedto be, for example, a series of nucleotides or a series of amino acids.The series of nucleotides are, for example, at least part of one chainof a pair of polymer chains constituting DNA (deoxyribonucleic acid), atleast part of the polymer chain constituting RNA (ribonucleic acid), orat least part of a gene. The sequence of the series of nucleotide can beconsidered as the sequence of bases each of which is included in eachnucleotide. On the other hand, the series of amino acids are at leastpart of the sequence of amino acids constituting a certain protein, forexample.

Provided that the entire number of the biological compounds is NT andeach biological compound is expressed in one character (e. g. onealphabet letter) of ASCII code (ANSI form) or Unicode, the size of thetotal text data corresponding to the sequence of the biologicalcompounds becomes NT bytes or 2 NT bytes, respectively. In thisestimation, the codes such as space, numerals, return, etc., which areused to make the sequence easy to read, are left out. Then, in the caseof FIG. 7, for example, the text data is divided into plural partialtext data T(i,j) arranged in N columns (i=1 to N) in the arrangeddirection and in M rows (j=1 to M) in the non-arranged direction. Eachof the partial text data T(i,j) is then converted into m-bit partialdata A(i,j) as shown in FIG. 8. Each of the m-bit partial data A(i,j)represents the sequence of n (n=16 in the case of FIG. 8) consecutivebiological compounds.

In this case, the simplest way of expressing the partial data A(i,j) isto use the partial text data T(i,j) itself that can be considered asnumerical data. That is, when the text data is recorded in ASCII codes,the ASCII codes can be used as the partial data A(i,j). When the textdata is recorded in Unicode, the codes in which each character isexpressed in the upper one-byte code of the corresponding two-byteUnicode may be used as the partial data A(i,j). However, it ispreferable that the partial text data T(i,j) is converted to a numericaldata block by using a conversion table (a predetermined rule) in whicheach character representing a biological compound is converted tonumerical data with six bits or less, for example, and the numericaldata block is considered as the partial data A(i,j) in order to reducethe amount of data to be processed.

Next, plural pieces of data approximately representing the sequenceinformation on each column and each row are computed by performingoperations to each of the m-bit partial data A(i,j) in the non-arrangeddirection and the arranged direction, respectively. For the computationwe need a field in which addition, subtraction, multiplication, anddivision of m-bit data can be performed. In a first method of thepresent invention Galois field (extension Galois field) GF(2^(m)) isused as the field. One advantage of using Galois field GF(2^(m)) is thatthe sequence information can be recorded concisely in small amounts ofdata, because when a piece of information is obtained by performingpredetermined operations (the first and second operations) of addition,subtraction, multiplication, and division to the m-bit partial dataA(i,j) of each column and each row respectively and, if necessary, m-bitcoefficients, the size of the piece of information (which is referred toas “parity information” in the present invention) is m bits.

Provided that the field represented by numbers modulo 2 (i.e. 0 and 1)is denoted by Z₂, the operations on Galois field GF(2^(m)) can bedefined by using an irreducible polynomial GF(X) of m-th degree withcoefficients defined on the field Z₂. That is, suppose that two m-bitpartial data A(i,j) and A(i′,j′) are expressed as numbers (a_(m−1)a_(m−2) . . . a₁ a₀) and (b_(m−1) b_(m−2) . . . b₁ b₀) (a_(k) and b_(k)are 0 or 1) respectively in binary notation, then these numbers areconverted to the following polynomials AF(X) and BF(X) whose degree islower than or equal to (m−1):AF(X)=a _(m−1) ·X ^(m−1) +a _(m−2) ·X ^(m−2) + . . . +a ₁ ·X+a ₀,   (1)BF(X)=b _(m−1) ·X ^(m−1) +b _(m−2) ·X ^(m−2) + . . . +b ₁ ·X+b ₀.   (2)

In this case, in order to add AF(X) and BF(X) together on Galois fieldGF(2^(m)), we have only to add the coefficients a_(k) and b_(k) of eachdegree k (k=0 to (m−1)) together on the field Z₂. Addition andsubtraction yield the same result on the field Z₂. Consequently, thecoefficients expressed in binary notation of the resultant polynomialare the result in vector representation obtained by adding the partialdata A(i,j) and A(i′,j′) together on Galois field GF(2^(m)). This is thesame result as is obtained by performing a bit-wise exclusive-ORoperation to the two coefficients of each degree.

Then, in order to multiply AF(X) by BF(X) on Galois field GF(2^(m)), theproduct is computed first by performing ordinary multiplication, and apolynomial CF(X) is obtained as the remainder (c_(k) is 0 or 1) bydividing the product by the irreducible polynomial GF(X) as follows.This operation is called the multiplication modulo the irreduciblepolynomial GF(X). In this calculation, addition (subtraction) of thecoefficients of each degree of X is performed on the field Z₂.CF(X)=c _(m−1) ·X ^(m−1) +c _(m−2) ·X ^(m−2) + . . . +c ₁ ·X+c ₀   (3)

The coefficients (c_(m−1 C) _(m−2). . . c₁ c₀) in binary notation of thepolynomial CF(X) are the result obtained by multiplying the partial dataA(i,j) by the partial data A(i′,j”) on Galois field GF(2^(m)). Moreover,suppose that an arbitrary m-bit coefficient is β, then the coefficient βis expressed as a polynomial DF(X) whose degree is less than or equal to(m−1) similar to equation (2). Therefore, in order to multiply thepartial data A(i,j) by the coefficient β, we have only to compute theproduct of the polynomial AF(X) of equation (1) and the polynomial DF(X)modulo the irreducible polynomial GF(X). Furthermore, in order to dividethe partial data A(i,j) by the coefficient β, for example, we have onlyto multiply the partial data A(i,j) by the inverse element β⁻¹ of β.

Therefore, all m-bit data (which include all partial data A(i,j)) can beconsidered as the elements of Galois field GF(2^(m)) in vectorrepresentation, and all m-bit data can be expressed in the polynomialssimilar to equation (1) whose degree is less than or equal to (m−1) inpolynomial representation. Moreover, when a set of m-bit data in vectorrepresentation are converted to a series of characters using theinverted relation of the conversion table (a predetermined rule) whichallocates the partial data A(i,j) to biological compounds (a string ofcharacters), the series of biological compounds corresponding to thedata are obtained.

According to this aspect of the invention, for example, as shown in FIG.8, the plural partial data A(i,j) are arranged in N columns (i=1 to N)in the arranged direction and in M rows (j=1 to M) in the non-arrangeddirection, and a first set of parity information (B1(i), B2(i), B3(i))are obtained for each column and a second set of parity information(C1(j), C2(j), C3(j)) are obtained for each row. Each piece of parityinformation (for example, B1(1)) of these two sets of parity informationis represented by m-bit data as well as one partial data A(i,j).

In this case, the amount of data DT1 of all the partial data A(i,j) isas follows:DT 1=m·N·M(bits).   (4)

In addition, provided that each of the first and second sets of parityinformation includes e pieces of parity information (e is an integerlarger than or equal to one), the amount of data DS1 of all the parityinformation is as follows. Here, when e pieces of parity information areincluded, up to e partial data A(i,j) can be recovered for each columnand each row, respectively.DS 1=m·e·(N+M)(bits)   (5)

Therefore, if it is assumed that the biological compounds arenucleotides constituting DNA and N=64, M=128, and e=2, the amount ofdata DT1 and DS1 are as follows from equations (4) and (5):DT 1=m·8192(bits),   (6)DS 1=m·384(bits)≈DT 1/20.   (7)

The amount of data of the parity information is therefore reduced toalmost {fraction (1/20)} of that of all the partial data A(i,j). In thismethod, because the sequence of the DNA in each chromosome of humans isexpressed as the text data of nearly 50-250 MB, if the text data isdivided into 500-2500 blocks and two sets of parity information arecomputed for each block, the amount of data of all the parityinformation will be reduced to nearly {fraction (1/20)} of that of thetext data, i.e. nearly from 2.5 MB to 12.5 MB quantity. Moreover, if thequantity of the partial data A(i,j) is 1/f of that of the text data, forexample, the quantity of the parity information will be reduced to 1/fof the above estimation.

According to this aspect of the invention, the information (the parityinformation) expressing the original sequence information of thebiological compounds approximately can be recorded in a file with lessdata than that of the original text data. Such a small amount of datacan be recorded in the mediums with small memory capacity, which can beeasily played by ordinary computers, such as a CD-ROM and flash-ROMbesides the mediums with large memory capacity such as a DVD-ROM. Andsince a small amount of data can be transmitted in a short time via acommunications network, the parity information can be offered to usersat low prices via cellular phone systems, for example.

Then users can identify the differences between two sequences ofbiological compounds easily using the first and second sets of parityinformation. In addition, provided that the number of the differences ineach column or row is less than or equal to e, the sequencecorresponding to the differences can be recovered by using the parityinformation.

Furthermore, as the file in which text data is recorded can becompressed by using conventional compression techniques (ZIP file, LHAfile, etc.), the file in which the parity information of the inventionis recorded can be compressed by using conventional compressiontechniques. However, it is very useful to reduce the size of theoriginal file, for when a compressed file is used, it must bedecompressed to its original file.

Then, in the first method for recording sequence information, when it isassumed that a is a primitive element of Galois field GF(2^(m)), forexample, the first set of parity information includes the sum of pluralproducts obtained by multiplying a set of the partial data (A(i,j)) ofeach column along the non-arranged direction by α^(sp), α^(s(p+1)),α^(s(p+2)), . . . , α^(s(p+dp)), where s and p are nonnegative integersand dp is an integer lager than or equal to one; and the second set ofparity information includes the sum of plural products obtained bymultiplying a set of the partial data (A(i,j)) of each row along thearranged direction by α^(tq), α^(t(q+1), α) ^(t(q+2)), . . . ,α^(t(q+dq)), where t and q are nonnegative integers and dq is an integerlager than or equal to one.

In this case, assuming that p=q=0, the first set of parity informationB1(i) and the second set of parity information C1(j) can be computedrespectively by the following operations on Galois field GF(2^(m)). TheΣ of equation (8) denotes the summation over the range 1 to M of j, andthe Σ of equation (9) denotes the summation over the range 1 to N of i.B 1(i)=Σα^(s(j−1)) ·A(i,j)=A(i,1)+α^(s) ·A(i,2)+α^(2s) ·A(1,3)+ . . .+α^((M−1)s) ·A(i,M)   (8)C 1(j)=Σα^(t(i−1)) ·A(i,j)=A(1,j)+α^(t) ·A(2,j)+α^(2t) ·A(3,j)+ . . .+α^((N−1)t) ·A(N,j)   (9)

Then, assuming that s=t=0 in equations (8) and (9), each of the parityinformation B1(i) and C1(j) reduces to the sum of the partial dataA(i,j) on Galois field GF(2^(m)), that is, the value obtained byperforming the exclusive-OR operation to the partial data A(i,j) of eachcolumn or row, respectively. Thus, the approximative information on thesequences of each column and each row is obtained by performing simpleoperations. However, in this case, if two partial data A(i,j) areexchanged in each column or each row, the value of the parityinformation B1(i) or C1(j) remains the same, respectively.

Then, assuming that s=t=1, the parity information B1(i) or C1(j) is thesum of the products obtained by multiplying the partial data A(i,j) ofeach column or row, respectively, by 1, α, α², α³, . . . . In this case,if two partial data A(i,j) are exchanged in each column or each row, thevalue of the parity information B1(i) or C1(j) varies, respectively. Asa result, the differences between two sequences of biological compounds,for example, can be identified more precisely. And, in order to multiplytwo partial data in each column or each row by mutually differentcoefficients using a certain s (≠0) (or t (≠0)), the coefficientsα^(s(j−1)) (or α^(t(i−1))) should differ from each other. For this,provided that a is a primitive element of Galois field GF(2^(m)), wehave only to assume that the number of the partial data A(i,j) of eachcolumn or each row is less than or equal to (2^(m−)1)/s (or(2^(m−)1)/t). That is, the size of the sequence of biological compoundsto be treated will be the largest by assuming that α is a primitiveelement.

When two sequences of biological compounds are compared, one partialdata A(i,j) that differs from the counterpart in each column and eachrow is recovered correctly using one piece of parity information in eachcolumn and each row, respectively. Accordingly, for example, the SNP(Single Nucleotide Polymorphism) of genes can be easily detected and thenormal sequence corresponding to it can be easily recovered.

Furthermore, in order to recover s′ and t′ partial data A(i,j) differingfrom the counterparts in each column and each row (s′ and t′ areintegers larger than or equal to two), respectively, the first set ofparity information (B1(i), B2(i), B3(i)) should include s′ sums computedfor mutually different values of the integer s for each of the pluralcolumns and the second set of parity information (C1(j), C2(j), C3(j))should include t′ sums computed for mutually different values of t foreach on the plural rows. In order to recover the partial data differingfrom the counterparts, we have only to solve simultaneous first-degreeequations with s′ (t′) unknown numbers on Galois field GF(2^(m)).

Moreover, in this aspect of the invention, the number of the second setof parity information may be made smaller than the number of the firstset of parity information by making the number of the partial dataplaced in the arranged direction smaller than the number of the partialdata placed in the non-arranged direction.

Especially, when the parity information of this aspect of the inventionis displayed on a monitor, the number of the partial data placed in thearranged direction may be reduced to the number corresponding to thewidth of the monitor, and the number of the partial data placed in thenon-arranged direction may be increased. In this case, the sequenceinformation can be displayed efficiently and plainly because the partialdata placed in the non-arranged direction can be easily displayed on themonitor by scrolling it up and down on the screen of the monitor.

However, when the number of the partial data placed in the arrangeddirection is smaller than that of the partial data placed in thenon-arranged direction, if the quantities of the first and second parityinformation are the same, the amount of data of the parity informationincreases as a whole. Thus, the amount of data of the parity informationcan be reduced and the differences between two sequences can berecovered efficiently by making the number of the parity information inthe arranged direction (the second set of parity information) smallerthan the number of the parity information in the non-arranged direction(the first set of parity information).

Moreover, the number of the partial data in the non-arranged directionis preferably smaller than or equal to (2^(m−)1)/4. As a result, sincethe partial data in the non-arranged direction can be multiplied by fourdifferent coefficients (α^(k), α^(2k), α^(3k), α^(4k)), up to fourdifferences (differences in the non-arranged direction) between twosequences for each column can be accurately recovered. This recoveryseems to be enough for the detection and the like of ordinary SNP.

Moreover, in this aspect of the invention, the integer m, which definesGalois field GF(2^(m)), is preferably a multiple of 64. Since thecomputers whose processing unit is 64 bits are increasing recently, theparity information can be efficiently computed by assuming that theinteger m is a multiple of 64.

Then, the first method may further include the following steps: assumingthat the sequence of the biological compounds is a standard sequence;computing two sets of parity information on a sequence of biologicalcompounds under inspection correspondingly to the two sets of parityinformation on the standard sequence; and identifying the differencesbetween the standard sequence and the sequence of biological compoundsunder inspection by using the four sets of parity information.Accordingly, the positions of the differences can be easily detected bycomparing two sets of parity information on the standard sequence andtwo sets of parity information on the sequence under inspection. Inaddition, provided that the number of the differences for each columnand each row is smaller than or equal to a predetermined number, thepart of the standard sequence corresponding to the differences can berecovered correctly by solving the simultaneous equations based on foursets of parity information and the sequence of biological compoundsunder inspection.

According to another aspect of the invention, a device for recordingsequence information on biological compounds, comprises the followingcomponents:

-   -   a sequencer (4) for reading sequence information on the        biological compounds;    -   dividing means (10, step 105) for dividing the text data        representing the sequence of the biological compounds or the        numerical data obtained by converting the text data based on a        conversion rule into plural m-bit partial data (A(i,j)) arranged        in plural columns in the arranged direction corresponding to the        direction along which the biological compounds are placed and in        plural rows in the non-arranged direction which crosses the        arranged direction, where m is an integer larger than or equal        to 16;    -   computing means (10, step 106) for computing a first set of        parity information by applying a first operation of Galois field        GF(2^(m)) along the non-arranged direction to a set of the        partial data of each column and computing a second set of parity        information by applying a second operation of Galois field        GF(2^(m)) along the arranged direction to a set of the partial        data of each row; and    -   recording means (15) for recording the first and second sets of        parity information in a recording medium.

According to the device, the first method for recording sequenceinformation on biological compounds such as nucleotides, amino acids,etc. can be carried out.

In the device for recording sequence information, when it is assumedthat a is a primitive element of Galois field GF(2^(m)), for example,the first set of parity information includes the sum of plural productsobtained by multiplying a set of the partial data (A(i,j)) of eachcolumn along the non-arranged direction by α^(sp), α^(s(p+1)),α^(s(p+2)), . . . , α^(s(p+dp)), where s and p are nonnegative integersand dp is an integer lager than or equal to one; and the second set ofparity information includes the sum of plural products obtained bymultiplying a set of the partial data of each row along the arrangeddirection by α^(tq), α^(t(q+1)), α^(t(q+2)), . . . , α^(t(q+dq)), wheret and q are nonnegative integers and dq is an integer lager than orequal to one.

Accordingly, the operations can be simplified because the coefficient bywhich the partial data (A(i,j)) is multiplied can be computed using onlythe primitive element α.

According to another aspect of the invention, a computer-readable medium(16) storing sequence information on biological compounds, comprises adata structure stored in the medium, wherein in order to form the datastructure,

-   -   the text data representing the sequence of the biological        compounds or the numerical data obtained by converting the text        data based on a conversion rule is divided into plural m-bit        partial data arranged in plural columns in the arranged        direction corresponding to the direction along which the        biological compounds are placed and in plural rows in the        non-arranged direction which crosses the arranged direction,        where m is an integer larger than or equal to 16;    -   a first set of parity information is computed by applying a        first operation of Galois field GF(2^(m)) along the non-arranged        direction to a set of the partial data of each column and a        second set of parity information is computed by applying a        second operation of Galois field GF(2^(m)) along the arranged        direction to a set of the partial data of each row; and    -   the first and second sets of parity information are recorded in        the data structure as the sequence information on the biological        compounds.

According to the computer-readable medium, the parity informationapproximately representing the sequence information on biologicalcompounds such as nucleotides and amino acids can be recorded in themedium in small amounts of data. Thus, such mediums as a CD-ROM, CD-R,flash-ROM, etc. whose memory capacity is relatively low but which areeasy to use can also be used as the computer-readable medium.

In the computer-readable medium, the data structure preferably furtherincludes a mathematical digest (message digest) of the text datarepresenting the sequence of the biological compounds or the numericaldata corresponding to the text data, where the size of the mathematicaldigest is larger than or equal to 40 bits.

The mathematical digest can be computed by applying a hash function suchas the MD5 hash function (the size of the message digest is 128 bits) orthe SHS (Secure Hash Standard) hash function (the size of the messagedigest is 160 bits) to the text data or the numerical data correspondingto the sequence of the biological compounds. It is easily confirmed withhigh accuracy whether two huge sequences of biological compounds are thesame or not using the digest. Furthermore, after recovering the partialdata differing from the counterparts by the use of the parityinformation, it can be confirmed whether the data has been recoveredcompletely or not by comparing the mathematical digests. If the size ofthe mathematical digest is larger than or equal to 40 bits, for example,the sequence information of the nucleotides of the entire human race canbe expressed almost without collisions.

In this aspect of the invention, when the integer m, which definesGalois field GF(2^(m)), is a multiple of 64, the hash function whosemessage digest is of the size of a multiple of 64 bits, e.g. the MD5hash function, is preferably used. In this case the calculation can beperformed efficiently.

According to another aspect of the invention, a first method -forsupplying sequence information on biological compounds comprises thefollowing steps:

-   -   as the procedure of a supplier (2A), recording the text data        representing the sequence of the biological compounds or the        numerical data obtained by converting the text data based on a        conversion rule in a first file (19) (step 104);    -   dividing the text data recorded in the first file or the        numerical data recorded in the first file into plural m-bit        partial data arranged in plural columns in the arranged        direction corresponding to the direction along which the        biological compounds are placed and in plural rows in the        non-arranged direction which crosses the arranged direction,        where m is an integer larger than or equal to 16;    -   computing a first set of parity information (B1(i) to B3(i)) by        applying a first operation of Galois field GF(2^(m)) along the        non-arranged direction to a set of the partial data of each        column and computing a second set of parity information (C1(j)        to C3(j)) by applying a second operation of Galois field        GF(2^(m)) along the arranged direction to a set of the partial        data of each row (steps 105,106);    -   recording the first and second sets of parity information in a        second file (20) (step 107); and    -   as the procedure of a user (2B), receiving the two sets of        parity information recorded in the second file through a        communications network (1) from the supplier (steps 110, 129).

According to the method for supplying sequence information, theabove-mentioned method for recording sequence information on biologicalcompounds is applied to a business model for supplying (selling) thesequence information thereon. That is, provided that the supplier hasread the sequence of biological compounds such as nucleotides of the DNAor amino acids of the protein of a certain organism X first, thesupplier computes the parity information approximately representing thesequence information in small amounts of data using the text data (ornumerical data converted therefrom), then supplies the parityinformation to the user via the communications network. As noted above,since the size of the parity information is about {fraction (1/20)} ofthat of the original text data, for example, the parity information canbe received in a short time via the communications network.

The first method for supplying sequence information further preferablyincludes the following steps:

-   -   as the procedure of the user, identifying the differences        between the sequence of the biological compounds held by the        supplier and the sequence of biological compounds subject to        examination based on the two sets of parity information (steps        130, 131); and    -   when the differences cannot be recovered, the user receiving the        sequence information on the part corresponding to the        differences within the text data recorded in the first file or        the numerical data recorded in the first file through the        communications network from the supplier (step 135).

If the detection and recovery of the differences between the sequenceunder inspection and the sequence of the supplier can be performed usingonly the parity information, there is no need to purchase moreinformation. On the other hand, when many differences exist and all ofthe corresponding sequences cannot be recovered correctly by using onlythe parity information, the user may purchase only the part of the textdata which part cannot be recovered correctly. Consequently, necessaryinformation is purchased through the communications network in a shorttime, and a relatively low-speed communications network like thecellular phone system can be used as the communications network.

In the method for supplying sequence information, when it is assumedthat α is a primitive element of Galois field GF(2^(m)), for example,the first set of parity information includes the sum of plural productsobtained by multiplying a set of the partial data of each column alongthe non-arranged direction by α^(sp), α^(s(p+1)), α^(s(p+2)), . . . ,α^(s(p+dp)), where s and p are nonnegative integers and dp is an integerlager than or equal to one; and the second set of parity informationincludes the sum of plural products obtained by multiplying a set of thepartial data of each row along the arranged direction by α^(tq),α^(t(q+1)), α^(t(q+2)), . . . , α^(t(q+dq)), where t and q arenonnegative integers and dq is an integer lager than or equal to one.

The user can detect the SNP (Single Nucleotide Polymorphism) and thelike easily using the parity information.

The method for supplying sequence information further preferablyincludes the following steps:

-   -   as the procedure of the supplier, letting the information on the        number of the sequence of the biological compounds and the        information on a mathematical digest of the text data or the        numerical data be disclosed to the public through the        communications network; and    -   as the procedure of a user, accessing the information on the        number of the sequence of biological compounds and the        information on the mathematical digest through the        communications network before receiving the two sets of parity        information (step 121).

Accordingly, after computing the digest (message digest) of the textdata (or numerical data converted therefrom) of the sequence ofbiological compounds of the organism X, the supplier discloses thedigest on the Internet, for example. Thus, the supplier can assert thathe is the first to read the sequence of the biological compounds of theorganism X without disclosing the original text data, and the user canavoid purchasing the same sequence information from different suppliers.

Moreover, after purchasing the sequence information on the biologicalcompounds from the supplier, a user computes the message digest of thepurchased sequence information by applying the hash function and obtainsthe size of the sequence. Then, by comparing the size and the messagedigest with the corresponding values disclosed on the Internet, the usercan check whether the purchased data is correct with high accuracy.

In the method for supplying sequence information, it is preferable thatthe size of the mathematical digest is 40 to 192 bits and the supplierfurther lets the information on a prescribed part of the sequence of thebiological compounds be disclosed to the public through thecommunications network. By comparing the prescribed part, for examplethe top and end sequences of about 8 biological compounds with thecorresponding sequences as well as the mathematical digest and the sizeof the sequence, the user can check whether the purchased data is thesame as the original data with higher accuracy.

According to another aspect of the invention, a second method forrecording sequence information on biological compounds comprises thefollowing steps:

-   -   dividing the text data representing the sequence of the        biological compounds or the numerical data obtained by        converting the text data based on a conversion rule into plural        m-bit partial data (A(i,j)) arranged in plural columns in the        arranged direction corresponding to the direction along which        the biological compounds are placed and in plural rows in the        non-arranged direction which crosses the arranged direction,        where m is an integer larger than or equal to 16;    -   assuming that a maximum value of the partial data is Nmax and a        prime number larger than the maximum value Nmax is P;    -   computing a first set of parity information by applying a first        operation of Galois field GF(P) along the non-arranged direction        to a set of the partial data of each column;    -   computing a second set of parity information by applying a        second operation of Galois field GF(P) along the arranged        direction to a set of the partial data of each row; and    -   representing the sequence information on the biological        compounds by the first and second sets of parity information.

In this aspect of the invention, the biological compounds are supposedto be, for example, a series of nucleotides or a series of amino acids.The series of nucleotides are, for example, at least part of one chainof a pair of polymer chains constituting certain DNA, at least part ofthe polymer chain constituting certain RNA, or at least part of a gene.Then, in the case of FIG. 7, for example, the text data representing thesequence information on the biological compounds is divided into pluralpartial text data T(i,j) arranged in N columns (i=1 to N) in thearranged direction and in M rows (j=1 to M) in the non-arrangeddirection. Each of the partial text data T(i,j) is then converted intom-bit partial data A(i,j) as shown in FIG. 8. Each of the m-bit partialdata A(i,j) represents the sequence of n (n=16 in the case of FIG. 8)consecutive biological compounds.

Next, plural pieces of data approximately representing the sequenceinformation on each column and each row are computed by performingoperations to each of the m-bit partial data A(i,j) in the non-arrangeddirection and the arranged direction, respectively. For the computationwe need a field in which addition, subtraction, multiplication, anddivision of m-bit data can be performed. In a second method of thepresent invention Galois field GF(P) is used as the field. When Galoisfield GF(P) is used and the maximum value of the partial data A(i,j) is(2^(m−)1), the prime number P needs to be an (m+1)-bit quantity. Thus,since a piece of information (which is referred to as “parityinformation” in the present invention) obtained by performingpredetermined operations on Galois field GF(P) to the partial data ofeach column and each row respectively is expressed as an (m+1)-bitnumber, the size of each parity information increases by one bit.However, as a whole, the original sequence information is approximatelyrepresented by a set of parity information whose total size is almost assmall as that obtained by using Galois field GF(2^(m)). Moreover,according to this aspect of the invention, the operations used tocompute the parity information are simpler than those on Galois fieldGF(2^(m)).

In this aspect of the invention, the detection and recovery of thedifferences between two sequences can also be performed to some degreeby comparing two sets of parity information of the two sequences.

In the second method for recording sequence information, the maximumvalue Nmax of the partial data is preferably smaller than (2^(m−)1). Theeasiest way of realizing this is to use the text data itselfcorresponding to the partial data A(i,j) as the partial data, which textdata is considered as numerical data. In this case, the prime number Ppreferably satisfies the following condition:2^(m)>P>Nmax.   (A1)

This means that the prime number P is an m-bit number larger than themaximum value Nmax. Accordingly, since each of the parity information isexpressed as m-bit data, the operations are simpler than those on Galoisfield GF(2^(m)) and the size of all the parity information is the sameas that obtained using Galois field GF(2^(m)) at the same time.

In the second method for recording sequence information, when it isassumed that δ is a primitive element of Galois field GF(P), forexample, the first set of parity information includes the sum of pluralproducts obtained by multiplying a set of the partial data of eachcolumn along the non-arranged direction by δ^(sp), δ^(s(p+1)),δ^(s(p+2)), . . . , δ^(s(p+dp)), where s and p are nonnegative integersand dp is an integer lager than or equal to one; and the second set ofparity information includes the sum of plural products obtained bymultiplying a set of the partial data of each row along the arrangeddirection by δ^(tq), δ^(t(q+1)), δ^(t(q+2)), . . . , δ^(t(q+dq)), wheret and q are nonnegative integers and dq is an integer lager than orequal to one. Accordingly, the parity information for each column andeach row can be computed easily by adjusting the values of the integerss and t.

According to another aspect of the invention, a second method forsupplying sequence information on biological compounds comprises thefollowing steps:

-   -   as the procedure of a supplier (2A), recording the text data        representing the sequence of the biological compounds or the        numerical data obtained by converting the text data based on a        conversion rule in a first file (19) (step 104);    -   dividing the text data recorded in the first file or the        numerical data recorded in the first file into plural m-bit        partial data arranged in plural columns in the arranged        direction corresponding to the direction along which the        biological compounds are placed and in plural rows in the        non-arranged direction which crosses the arranged direction,        where m is an integer larger than or equal to 16;    -   assuming that a maximum value of the partial data is Nmax and a        prime number larger than the maximum value Nmax is P;    -   computing a first set of parity information by applying a first        operation of Galois field GF(P) along the non-arranged direction        to a set of the partial data of each column and computing a        second set of parity information by applying a second operation        of Galois field GF(P) along the arranged direction to a set of        the partial data of each row;    -   recording the first and second sets of parity information in a        second file (20); and    -   as the procedure of a user (2B), receiving the two sets of        parity information recorded in the second file through a        communications network (1) from the supplier.

According to the second method for supplying sequence information, theabove-mentioned second method for recording sequence information onbiological compounds is applied to a business model for supplying(selling) the sequence information thereon. That is, provided that thesupplier has read the sequence of biological compounds such asnucleotides of the DNA or amino acids of the protein of a certainorganism X first, the supplier computes the parity informationapproximately representing the sequence information in small amounts ofdata using the text data (or numerical data converted therefrom), thensupplies the parity information to the user via the communicationsnetwork. In this method, since the amount of the parity information canbe reduced to almost the same degree compared to the original text dataas that computed using Galois field GF(2^(m)), the parity information isreceived in a short time via the communications network.

The second method for supplying sequence information further preferablyincludes the following steps:

-   -   as the procedure of the user, identifying the differences        between the sequence of the biological compounds held by the        supplier and the sequence of biological compounds subject to        examination based on the two sets of parity information; and    -   when the differences cannot be recovered, the user receiving the        sequence information on the part corresponding to the        differences within the text data recorded in the first file or        the numerical data recorded in the first file through the        communications network from the supplier.

If the detection and recovery of the differences between the sequenceunder inspection and the sequence of the supplier can be performed usingonly the parity information, there is no need to purchase moreinformation. On the other hand, when many differences exist and all ofthe corresponding sequences cannot be recovered correctly by using onlythe parity information, the user may purchase only the part of the textdata which part cannot be recovered correctly. Consequently, necessaryinformation is purchased through the communications network in a shorttime, and a relatively low-speed communications network like thecellular phone system can be used as the communications network.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a computer system used in a preferredembodiment of the invention;

FIG. 2 is a diagram of a part of DNA processed in the preferredembodiment and an expression of the nucleotide sequence of the part ofDNA in binary notation;

FIG. 3 is a flow chart showing part of the procedure of a DNAinformation supplier in the preferred embodiment;

FIG. 4 is a flow chart of the procedure of the supplier following thesteps of FIG. 3;

FIG. 5 is a flow chart showing part of the procedure a user of DNAinformation in the preferred embodiment;

FIG. 6 is a flow chart of the procedure of the user following the stepsof FIG. 5;

FIG. 7 is a diagram showing the text data of the nucleotide sequence(2048 nucleotides) of a standard sample E (DNA) where the text data isdivided into plural partial text data T(i,j) in 4 columns and 32 rows;

FIG. 8 is a diagram of the partial data A(i,j) of the standard sample Eand the parities B1(i) to C3(j) computed therefrom;

FIG. 9 is a diagram showing the text data of the nucleotide sequence(2048 nucleotides) of a sample F (DNA) where the text data is dividedinto plural partial text data TF(i,j) in 4 columns and 32 rows;

FIG. 10 is a diagram of the partial data AF(i,j) of the sample F and theparities B1F(i) to C3F(j) computed therefrom;

FIG. 11 is a diagram of the parities of the sample F differing from thecounterparts of the standard sample E and of the recovered partial data;

FIG. 12 is a flow chart showing the calculations for finding the valuesof the unknown data X1, X2, Y1, Y2 on Galois field GF(2¹²⁸);

FIG. 13 is a diagram showing the partial data B(i,j) arranged in 5columns and 13 rows, which partial data are obtained by dividing thebinary data converted from the text data of the nucleotide sequence ofthe standard sample E shown in FIG. 7;

FIG. 14 is a diagram showing the text data of the amino acid sequence(820 amino acids) of a sample G (protein) where the text data is dividedinto partial text data in 4 columns and 26 rows; and

FIG. 15 is a diagram of the parities B1G(i) to C3G(j) computed from theamino acid sequence of FIG. 14.

BEST MODE FOR CARRYING OUT THE INVENTION

A preferred embodiment of the present invention will now be describedwith reference to the accompanying drawings. In this embodiment of theinvention, some pieces of information on sequences of nucleotides(biological compounds) in DNA (deoxyribonucleic acid) are processed withcomputer systems.

Referring to FIG. 1, which illustrates a computer system 2A of theembodiment, the computer system 2A has on its center an informationprocessor 10 which consists of a CPU (central processing unit), memoriessuch as RAM, ROM, etc., and storage devices including hard disk drivesand the like. A display unit 12 consisting of a CRT display is connectedto the information processor 10 via a video RAM (VRAM) 11, and a CD-R/RWdrive 15 which can record data on a CD-Recordable disk (hereinafterreferred to as “CD-R”) 16 and read data in a CD-R and CD-ROM isconnected to the information processor 10 via an I/O unit (input-outputunit) 14. As a mass storage device a magnetic disk unit 17 with aboutseveral 100 GB memory is connected to the information processor 10 viathe I/O unit 14.

The operating system and the application program to process sequenceinformation on DNA as described below are installed in the hard diskdrive of the information processor 10 of this embodiment through theCD-R/RW drive 15. Moreover, though the CD-R 16 corresponds to thereadable medium of the present invention, a flash ROM, a flexible disk,a magneto-optical disk (MO), a digital video disc (DVD), a hard diskdrive (for example, one built into the server which can be accessedthrough the Internet), etc. can be used as the readable medium as wellas the CD-R and CD-ROM.

A keyboard 13 as the input device for character information, an opticalmouse 204 as the pointing device (input device), and a communicationcontrol unit 18 consisting of a router (or a modem and so on) are alsoconnected to the information processor 10. The mouse 204 comprises adisplacement signal generator 207 that generates a signal indicating theposition of a cursor on the screen of the display unit 12, a left switch204 a, and a right switch 204 b. Those switches 204 a, 204 b (signalgenerators) generate signals designating information to be selected andvarious commands, etc. The computer system 2A comprises the informationprocessor 10, the VRAM 11, the display unit 12, the keyboard 13, themouse 204, the I/O unit 14, the CD-R/RW drive 15, the magnetic diskunits 17, the communication control unit 18, etc. The Windows(registered trademark of Microsoft Corporation) is used as the operatingsystem in this embodiment. The present invention can also be applied tothe systems in which other operating systems such as UNIX (registeredtrademark of X/Open), OS/2 (registered trademark of IBM Corporation),MacOS (registered trademark of Apple Computer), and Linux (trademark orregistered trademark of Linus Torvalds) are used.

Furthermore, the computer system 2A (the information processor 10) isconnected to a communications network 1 consisting of the generaltelephone network via the communication control unit 18, and a provider3 that presents various contents, a computer system 2B, a large numberof servers (not shown), and other many computer systems (not shown) areconnected to the communications network 1. The computer systems 2A, 2Band the provider 3 can communicate with one another through the Internetconstructed on the communications network 1. In this embodiment, theowner of the computer system 2A is supposed to be a supplier (or aseller) of DNA information, and the owner of the computer system 2B issupposed to be a user (or a purchaser) of the DNA information. Thus, theapplication programs similar to those installed in the computer system2A to process sequence information on DNA are installed to the lattercomputer system 2B in advance.

Now, a sequencer (DNA Sequencer) 4 that reads the sequence of a seriesof nucleotides (or the sequence of bases) in DNA as a sequence reader isconnected to the information processor 10 in the computer system 2A ofthis embodiment through the I/O unit 14. The sequencer 4 reads thesequence of the nucleotides in one chain of a pair of polymer chainsthat constitute DNA using the Sanger method, for example. The Sangermethod is disclosed in, for example, the reference 1 (Maxim D.Frank-Kamenetskii: Unraveling DNA (the most important molecule of life,revised and updated), translated by Lev Liapin, Chapter 6 (pp. 59-70)(Perseus Books, 1997)). The sequencer 4 memorizes the just-read sequenceof the series of nucleotides in an internal mass storage device by theform of text data, and supplies the text data of a certain nucleotidesequence in the mass storage device to the information processor 10through the I/O unit 14 at the request of the information processor 10.Accordingly, the information processor 10 processes the text data bymeans of the application programs to process sequence information on DNAas follows. Here it should be noted that a database of sequenceinformation on nucleotides (or bases) constituting nucleic acids such asDNA and RNA (ribonucleic acid) can be used instead of the sequencer 4.

First of all, the first basic procedure of the information processor 10of this embodiment will be described. The information processor 10records the text data supplied by the sequencer 4 that represent thecertain nucleotide sequence of DNA in a master file 19 defined in themagnetic disk unit 17 as it is. The information processor 10 thenconverts the text data into the numerical data having less data than thetext data, and records the converted numerical data in a working file 20defined in the magnetic disk unit 17. In the following explanations, thenumber k in binary notation is described as bin(k) and the number inhexadecimal notation as hex(k).

In this case, DNA consists of four kinds of nucleotides, and thenucleotide including adenine, guanine, cytosine, or thymine as a base isrepresented respectively by the character A, G, C, or T in the text datasupplied by the sequencer 4. Furthermore, the ASCII code of one byte(eight bits) consisting of hex(41), hex(47), hex(43), or hex(54) isallocated respectively to the character A, G, C, or T. As for RNA, thenucleotide including uracil is represented by the character U (hex(55))instead of the nucleotide including thymine. Therefore, the text datarepresenting the sequence of n nucleotides (n is an integer) will amountto the data of n bytes. The sequence of n nucleotides can be consideredas the sequence of n bases (adenine, guanine, cytosine, and thymine (oruracil)).

In this embodiment, to express the text data by as less data as possiblewithout reducing the amount of information, four kinds of nucleotides inDNA are represented by mutually different two-bit data. In DNA, one pairof bases (adenine and thymine) are mutually complementary and the otherpair of bases (guanine and cytosine) are also mutually complementary. Itis thus supposed that a pair of nucleotides whose bases arecomplementary are mutually complementary, and a pair of data each ofwhich is the bit-wise complement of the other are allocated to one pairof complementary nucleotides including adenine and thymine respectively,and another pair of data each of which is the bit-wise complement of theother are allocated to the other pair of complementary nucleotidesincluding guanine and cytosine respectively. Table 1 (the conversiontable) is used to show the allocation of the data in this embodiment.Table 1 means that the character A, T (or U), G, or C in the text datarepresenting the sequence of nucleotides is replaced respectively bybin(00), bin(11), bin(01), or bin(10). TABLE 1 Nucleotide two-bit datanucleotide including adenine (A) bin(00) nucleotide including thymine oruracil (T or U) bin(11) nucleotide including guanine (G) bin(01)nucleotide including cytosine (C) bin(10)

According to this embodiment, each nucleotide is represented by two-bitdata, which is equivalent to representing each base by two-bit data.Moreover, the allocation of the data is not limited to Table 1. Forexample, the allocation may be used in which the nucleotide includingthymine or adenine is represented respectively by bin(00) or bin(11), orthe nucleotide including guanine or cytosine is represented respectivelyby bin(10) or bin(01). Besides, the data bin(01) and bin(10) may beallocated to the pair of nucleotides in which one includes adenine andthe other includes thymine, and the data bin(00) and bin(11) may beallocated to the pair of nucleotides in which one includes guanine andthe other includes cytosine. In the case of RNA, the same data that aregiven to the corresponding nucleotides in DNA are allocated to thenucleotides except that the data given to the nucleotide includingthymine is allocated to the nucleotide including uracil.

Suppose that the sequence information on nucleotides of the DNA molecule5 partly shown in FIG. 2 is processed in this embodiment. The sequenceinformation is a part of the sequence information on a series ofnucleotides of the DNA of Escherichia coli (E. coli), which was obtainedfrom the website 1 (ftp://ncbi.nlm.nih.gov/genbank/genomes/bacteria/)offered by NCBI (The National Center for Biotechnology Information).

Referring to FIG. 2, the DNA molecule 5 consists of a pair of polymerchains 6A and 6B (a double helix), where one polymer chain 6A comprisesfour kinds of nucleotides, i.e. the nucleotide 7A with adenine, thenucleotide 7G with guanine, the nucleotide 7C with cytosine, and thenucleotide 7T with thymine, and the other polymer chain 6B is thenucleotide sequence complementary to the chain 6A. The text datarepresenting the sequence of the polymer chain 6A are supplied to theinformation processor 10 of FIG. 1. The text data is supposed to be thedata of a string of characters: “AGCTTT . . . .” Accordingly, afterdividing the text data into blocks arranged in N columns and M rows (Nand M are both integers of two or larger), the information processor 10converts the characters A, G, C, and T in each block one by one intotwo-bit data using Table 1 (the conversion table). Thus, the informationprocessor 10 obtains the binary data BNA (=bin(0001101111 . . . )) asnumerical data. This binary data BNA is recorded in the working file 20defined in the magnetic disk unit 17 of FIG. 1. The binary data BNA isreduced to ¼ of the original text data.

In this case, the data showing which nucleic acid (DNA or RNA) isrecorded in the file, i.e. the data showing which character (T or U) thebin(11) should be interpreted as, the data showing the number ofnucleotides, and other necessary data are preferably recorded in the toppredetermined several bytes of the working file 20. Moreover, when thesize of the working file 20 is a multiple of 1 byte (8 bits) and thebinary data BNA have plural bytes and a fraction, the predetermineddummy data only have to be added to the end, which will hardly increasethe amount of data. Then, for example, when the user (the owner of thecomputer system 2B) sends a purchase order for the sequence informationon the DNA molecule 5 shown in FIG. 2 to the supplier (the owner of thecomputer system 2A), the data of the working file 20 is transmitted tothe computer system 2B as an email attachment through the communicationsnetwork 1 and a provider (not shown). In this case, the data of theworking file 20 may be transmitted as a compression file (ZIP file, LHAfile, etc.). The transmission time will be reduced to almost ¼ comparedwith the case when transmitting the original text data, since the dataof the working file 20 is reduced to almost ¼ of the original text data.Thus, the communication costs of both the supplier and the user can bereduced.

Next, when the user wants to recover the text data showing the sequenceof the polymer chain 6A in FIG. 2 from the received data of the workingfile 20, the computer system 2B will inversely convert the binary dataBNA of the working file 20 into a string of the characters A, G, C, andT (or U) one by one by using Table 1. Moreover, for example, when theuser needs also the text data showing the nucleotide sequence of theother complementary polymer chain 6B in FIG. 2, the computer system 2Bwill obtain the reversed binary data NOT(BNA) (=bin(1110010000 . . . ))as shown in FIG. 2 by getting the bit-wise complement of the binary dataBNA. The reversed binary data NOT(BNA) is the same as the binary dataBNB that is obtained by converting the text data (the string ofcharacters “TCGAAA . . . ”) which shows the nucleotide sequence of theother polymer chain 6B according to Table 1. Therefore, the computersystem 2B can obtain the text data of the sequence of the complementarypolymer chain 6B at an extremely high speed by inversely converting thereversed binary data NOT(BNA) into a string of the characters A, G, C,and T (or U) one by one according to Table 1. In this procedure, thebit-wise complement operation can be performed at an extremely highspeed in usual computers. Furthermore, the operation for obtaining thebit-wise complement of any data can be replaced by, for example, theoperation for computing the bit-wise exclusive-OR of the data andbin(111111 . . . ).

It should be noted that the supplier may record the content of theworking file 20 in the CD-R 16 by means of the CD-R/RW drive 15 and sendthe CD-R 16 to the user by mail instead of transmitting the data of theworking file 20 to the user through the communications network 1. Forexample, the sequence information on a complete set of human DNA (humangenome) is expressed as about 3 GB text data. The text data can beconverted into the binary data of ¾ GB, i.e. 750 MB as the numericaldata of this embodiment by using Table 1. Since the capacity of thecurrent CD-R and CD-ROM is about 650 MB, the binary data of about 750 MBcan be recorded easily in the CD-R 16 by compressing a part or all ofthe binary data. On the other hand, when the data of about 750 MB istransmitted through the communications network 1, it might sometimestake too much transmission time today.

Moreover, each amino acid is determined by a sequence of threenucleotides, i.e. a codon. One or more 6-bit data representing eachamino acid are thus obtained by expressing each nucleotide of the threenucleotides corresponding to the amino acid in 2-bit data. Then the datawith the smallest value of all the 6-bit data corresponding to eachamino acid may be chosen as the data representing the amino acid.Furthermore, since a piece of data whose size is a multiple of one byteis easy to handle, we may represent one amino acid by one-byte data thatis obtained by adding two-bit discrimination data before or behind the6-bit data. Accordingly, one advantage is that a set of common codes canbe used in representing both nucleotides and amino acids.

Then, the second basic procedure of the information processor 10 of thisembodiment will be described. In this embodiment, a mathematical digest(a message digest) is computed by applying a certain hash function tolarge text data (or the numerical data obtained by converting the textdata according to Table 1) that represents a nucleotide sequence. Inthis embodiment, the MD5 hash function proposed by R. Rivest is used asthe hash function. The MD5 hash function is disclosed in the website 2(http://www.kleinscmidt.com/edi/md5.htm) offered by the network workinggroup and Rivest. The algorithm of the MD5 hash function is alsodisclosed in WO 01/80431 A1. Moreover, the algorithms of the MD5 hashfunction and other hash functions disclosed in U.S. application Ser. No.10/272,107, filed Oct. 16, 2002, are incorporated herein by reference. A128-bit message digest is obtained by applying the MD5 hash function totext data (or a text file). In the future 64-bit CPUs will be used evenin usual computers. Message digests of 128(=2·64) bits will thus beprocessed very easily. Furthermore massage digests of 192(=3·64) bitswill also be processed easily.

In this embodiment, the program that was developed by RSA Data SecurityInc. and is disclosed in the website 2 is used to apply the MD5 hashfunction.

As an example for using the message digests, the supplier of sequenceinformation on DNA (or the information processor 10) reads thenucleotide sequence of DNA of a certain organism and computes themessage digest of the text data representing the nucleotide sequence byapplying the hash function. Then the supplier discloses the messagedigest on the Internet as well as the information showing the name ofthe organism and the location of the DNA. Consequently, the supplierseems to be able to declare that he was the first to decipher the DNAsequence of the organism without disclosing the whole text data.Afterwards, when a user sends a purchase order for the sequenceinformation, the supplier converts the text data representing thenucleotide sequence into binary data by using Table 1, and transmits thebinary data to the user, for example, by email through thecommunications network 1. Accordingly, the user inversely converts thebinary data into the text data by using Table 1, and computes themessage digest by applying the above-mentioned hash function to theinversely converted text data.

Furthermore, when both message digests computed by the user anddisclosed by the supplier are equal, it is guaranteed with high accuracythat the purchased sequence information is equal to the sequenceinformation held by the supplier. In addition, users can avoid buyingthe same pieces of sequence information from different suppliers bycomparing the massage digests disclosed by the suppliers. In this casethe accuracy with which two nucleotide sequences are equal can beimproved by further comparing the size of both nucleotide sequences andshort sequences, for example, top parts or end parts selected from bothnucleotide sequences.

As a hash function the SHS (Secure Hash Standard) hash function proposedby NBS (National Bureau of Standards) and disclosed in the reference 2(FIPS Publication 180,1993) can also be used. The SHS hash function hasmore complex operations than the MD5 hash function, and obtains themessage digest of 160 bits. Since the number of amino acids constitutinga protein, for example, is about 20-1000, and the text datacorresponding to the amino acid sequence can be expressed in as smallsize as about 20 bytes to 1 KB using one-Letter code, the text datamight be easily estimated from the message digest. Thus, when messagedigests of sequence information on amino acids are required, it issometimes desirable to use the SHS hash function to prevent users fromestimating the original text data.

Moreover, for example, when message digests need to be computed byapplying a certain hash function in order just to confirm that the twolarge amounts of text data representing nucleotide sequences are equal,the hash function does not seem to be necessarily the one that performsa series of complex mathematical operations repeatedly. In such anapplication, for example, the MD4 hash function disclosed in thereference 3 (R. L. Rivest: “The MD4 message digest algorithm”, LectureNotes in Computer Science, 537,303-311(1991)) may be used. Moreover, inorder just to confirm that the two sequences are equal, the size of themessage digest may be sometimes as short as 40-128 bits.

Then, referring to the flow charts in FIGS. 3-6, a business model ofthis embodiment will be described in detail in which the supplier of DNAinformation (the computer system 2A) sends the sequence information onDNA to the user (the computer system 2B) in FIG. 1. First of all, instep 101 in FIG. 3, the supplier of DNA information makes the sequencer4 read the nucleotide sequence of one chain of the DNA of a standardsample (hereinafter referred to as “the standard sample E”), and thetext data TX1 representing the just-read nucleotide sequence aresupplied to the information processor 10. In this embodiment, thestandard sample E is supposed to be E. coli, whose sequence data wasobtained from the website 1, and the text data showing the sequence ofthe first 2048 nucleotides of the DNA of E. coli is used as the textdata TX1 as shown in FIG. 7.

The DNA sequence of the standard sample E is shown in SEQ ID NO:1 inSequence Listing. The text data shown in FIG. 7 was generated byremoving all numerical data from the sequence in SEQ ID NO:1 andreplacing the characters a, g, c, and t respectively by the charactersA, G, C, and T in the sequence.

Then, in step 102, the information processor 10 obtains a 128-bitmessage digest AB1 by applying the above-mentioned MD5 hash function tothe supplied text data TX1. The information processor 10 then obtainsthe number NA1 of the nucleotides in the DNA sequence and two8-character nucleotide sequences ST1 and SB1 taken respectively from thetop and end portions of the text data TX1 as follows:AB 1=hex(849339ac244cde42b5346ab5989aab61),   (11)NA1=2048,ST1=AGCTTTTC, SB1=CGCGAAGG.

In the next step 103, the information processor 10 obtains the text dataTXR1 (=GGAAGC . . . TTTCGA) by rearranging the text data TX1 in reverseorder, and then obtains the message digest ABR1 by applying the MD5 hashfunction to the text data TXR1. In addition, the information processor10 obtains two 8-character nucleotide sequences STR1 and SBR1corresponding respectively to the top and end portions of the text dataTXR1 by rearranging the sequences SB1 and ST1 in reverse order. Thesevalues are as follows:ABR 1=hex(4eb1feae30f522642b912ce3ea09652b),   (12)STR1=GGAAGCGC, SBR1=CTTTTCGA.

Then, in step 104, the information processor 10 records the informationon the name of the standard sample E (the identifier of the sample), thenumber NA1, the text data TX1, the sequences ST1 and SB1, the messagedigest AB1, the reversed sequences STR1 and ABR1, and the message digestABR1 of the reversed sequence in the master file 19 defined in themagnetic disk unit 17. In this case, the master file 19 may be dividedinto two or more files, and the text data TX1 and other data may berecorded in different files. Moreover, for example, when the size of thetext data TX1 is more than or equal to about 100 MB, the text data TX1may be divided into plural parts recorded in different master files.

In the subsequent step 105, the information processor 10 divides thetext data TX1 of the standard sample E into plural partial text dataT(i,j) (i=1 to N, j=1 to M) with 16 characters so that the partial textdata T(i,j) are arranged in N columns in the arranged directioncorresponding to the direction along which nucleotides are placed and inM rows in the direction (hereinafter referred to as “the non-arrangeddirection”) normal to the arranged direction as shown in FIG. 7. Here,both of the numbers N and M are arbitrary integers larger than or equalto 2. As described above by referring to Equations 4 and 5, when thesize of the text data TX1 is about 100 KB (or any multiple thereof) andthe supplier needs the parity information whose size is reduced to about{fraction (1/20)} of that of the text data TX1, the values of N and Mare chosen such that N=64 and M=128, for example. In the followingdescription, for simplicity, the text data TX1 is supposed to be dividedin 4 columns and 32 rows, i.e. N=4 and M=32. In this case, no fractionis left. However, for example, if the number of characters of the lastpartial text data T(4,32) is smaller than 16 in FIG. 7, one or morepredetermined characters (for example, the character “A”) have only tobe added to the empty part of the last partial text data as dummy data.Moreover, the size of the partial text data T(i,j) may be other than 16characters. However, in order to improve the processing speed, the sizeof the partial text data T(i,j) is preferably any multiple of 8characters.

In addition, the information processor 10 converts each of the partialtext data T(i,j) with 16 characters in FIG. 7 into partial data A(i,j)which consists of 128(=16×8)-bit binary data (the numerical data)respectively based on a predetermined conversion table. In thisembodiment, a function asc(T(i,j)) is used as the conversion table,which function simply converts the partial text data T(i,j) into theASCII codes as follows:A(i,j)=asc(T(i,j))   (13)

It should be noted that the function asc(T(i,j)) converts the partialtext data T(i,j) so that the codes of the characters at the front andend of the partial text data are placed in the least and mostsignificant parts, respectively, as shown by the converted example ofT(3,11) in FIG. 7. In this case, if the partial data A(i,32) in the lastrow includes less than 128-bit code data, the dummy data such aspredetermined character codes or numerical data representing 0 (hex(000. . . )) is added to the most significant part of partial data.Consequently, all of the partial data A(i,j) are arranged in 4 columnsand 32 rows as shown in FIG. 8. Moreover, a set of data (the numericaldata) obtained by arranging all of the partial data A(i,j) consecutivelyin the direction corresponding to the direction along which nucleotidesare placed is referred to as the binary data BN1. The partial text dataT(i,j) in FIG. 7 has substantially the same amount of data as thepartial data A(i,j) in FIG. 8.

Then, in this embodiment, a certain operation on Galois field GF(2^(m))is applied to the partial data A(i,j) by considering the partial dataA(i,j) to be an element of Galois field GF(2^(m)) in vectorrepresentation. Since the size of the partial data A(i,j) of thisembodiment is 128 bits, the value of m is 128 (twice as large as 64) andGalois field GF(2¹²⁸) is used. Moreover, in this embodiment, thefollowing polynomials are used as an irreducible polynomial GF(X) and aprimitive element α on Galois field GF(2¹²⁸). Galois field GF(2^(m)) maybe called an extension Galois field.GF(X)=1+X ¹²¹ +X ¹²⁶ +X ¹²⁷ +X ¹²⁸   (14)α=X   (15)

GF(X) and α are expressed as bin(1110000100 . . . 01) and bin(00 . . .0010), respectively, in vector representation of Galois field GF(2¹²⁸).A polynomial (1+X) and the like can be used as the primitive element α.Moreover, the following irreducible polynomial GF′(X) can also be used,for example, as another irreducible polynomial on Galois field GF(2¹²⁸),and the following element α′ can be used as a primitive elementcorresponding to the irreducible polynomial GF′(X).GF′(X)=1+X ¹¹ +X ¹²⁴ +X ¹²⁵ +X ¹²⁶ +X ¹²⁷ +X ¹²⁸   (14A)α′=1+X+X ²   (15A)

Moreover, the easiest method of confirming the irreducibility of thepolynomial GF(X) is to divide the polynomial GF(X) by all possiblepolynomials whose degree is less than or equal to m′, where m′ is theinteger not exceeding m/2. In this method, if there is no polynomialdividing the polynomial without a remainder, the polynomial GF(X) isirreducible.

Furthermore, provide that the degree m is large, the irreducibility ofthe polynomial GF(X) can be confirmed, for example, by “the method ofKronecker” disclosed in reference 4 (Van der Waerden, B. L. (1953),Modern Algebra (2 vols.), p. 77, Ungar, N.Y.). A practical method ofconfirming the irreducibility of the polynomial GF(X) is to use thebuilt-in function “POLFACT2” in the “UBASIC”, which is a software forstudying the number theory and which is disclosed in website 3(http://archives.math.utk.edu/software/msdos/number.theory/ubasic/.html)or in website 4 (http://www.rkmath.rikkyo.ac.jp/˜kida/ubasic.htm).

Then, assuming that k=2^(m−)1, the primitive element α of Galois fieldGF(2^(m)) satisfies the following relations modulo the irreduciblepolynomial GF(X):α^(k)=1(mod GF(X)),   (16)α^(k′)≠1(mod GF(X))(1≦k′<k).   (17)

Suppose that the integer k can be factorized as follows using primenumbers p1, p2, . . . , pr and integers n1, n2, . . . , nr:k=2^(m−)1=p1^(n1) ·p2^(n2) . . . pr ^(nr).   (18)

Then, the primitive element α is determined so that all of α to thepower of (p1^(n1−1)·p2^(n2) . . . pr^(nr)), α to the power of(p1^(n1)·p2^(n2−1) . . . pr^(nr)), . . . and α to the power of(p1^(n1)·p2^(n2) . . . pr^(nr−1)) do not come to 1 modulo theirreducible polynomial GF(X).

Moreover, since an arbitrary nonzero element β of Galois field GF(2^(m))satisfies equation (16), the inverse element β⁻¹ of β can be computed asfollows by the use of k(=2^(m−)1):β⁻¹=β^(k−1)(mod GF(X)).   (16R)

Therefore, for example, when the partial data A(i,j) is divided by β, wehave only to multiply the partial data A(i,j) by β^(k−1).

In the next step 106, the information processor 10 computes the firstparity B1(i), the second parity B2(i), and the third parity B3(i) forthe partial data A(i,j) of each column (i=1 to 4) shown in FIG. 8 byadding up all the partial data A(i,j), calculating the sumΣα^((j−1))A(i,j), and calculating the sum Σα^(2(j−1))·A(i,j),respectively, along the non-arranged direction (j=1 to 32) of eachcolumn on Galois field GF(2¹²⁸). These parities B1(i) to B3(i) in thenon-arranged direction (the first set of parity information) areexpressed as follows using the primitive element α and by performing theoperations modulo the irreducible polynomial GF(X). The Σ in paritiesB1(i) to B3(i) denote the summation over the range 1 to 32 of j, and thefollowing equations are computed for the range 1 to 4 of i:B 1(i)=ΣA(i,j)=A(i,1)+A(i,2)+ . . . +A(i,32),   (19)B 2(i)=Σα^((j−1)) ·A(i,j)=A(i,1)+α·A(i,2)+ . . . +α³¹ ·A(i,32),   (20)B 3(i)=Σα^(2(j−1)) ·A(i,j)=A(i,1)+α² ·A(i,2)+ . . . +α⁶² ·A(i,32).  (21)

In this case, the parity B1(i) in equation (19) expressed in vectorexpression is the same as the result obtained by performing a bit-wiseexclusive-OR operation to the partial data A(i,j). The parities B2(i)and B3(i) in equations (20) and (21) are computed by representing eachpartial data A(i,j) by a polynomial like equation (1) whose degree isless than or equal to 127 (m=128) and performing the operations modulothe irreducible polynomial GF(X).

In addition, the information processor 10 computes the first parityC1(j), the second parity C2(j), and the third parity C3(j) for thepartial data A(i,j) of each row (=1 to 32) shown in FIG. 8 by adding upall the partial data A(i,j), calculating the sum Σα^((i−1))·A(i,j), andcalculating the sum Σα^(2(i−1))·A(i,j), respectively, along the arrangeddirection (i=1 to 4) of each row on Galois field GF(2¹²⁸). Theseparities C1(j) to C3(j) in the arranged direction (the second set ofparity information) are expressed as follows using the primitive elementα and by performing the operations modulo the irreducible polynomialGF(X). The Σ in parities C1(j) to C3(j) denote the summation over therange 1 to 4 of i, and the following equations are computed for therange 1 to 32 of j:C 1(j)=ΣA(i,j)=A(1,j)+A(2,j)+ . . . +A(4,j),   (22)C 2(j)=Σα⁽ i−1)·A(i,j)=A(1,j)+α·A(2,j)+ . . . +α³ ·A(4,j),   (23)C 3(j)=Σα^(2(i−1)) ·A(i,j)=A(1,j)+α² ·A(2,j)+ . . . +α⁶ ·A(4,j).   (24)

The parities B1(i) to B3(i) and C1(j) to C3(j) actually computed byusing the partial data A(i,j) are shown in vector representation ofhexadecimal notation in FIG. 8. In this embodiment, since the number ofthe parities B1(i) to B3(i) of each column and the number of theparities C1(j) to C3(j) of each row are three, respectively, up to threepartial data A(i,j) differing from the counterparts can be recoveredcorrectly for each column and each row by comparing two nucleotidesequences. Thus, if the detection (identification) of the partial dataA(i,j) differing from the counterparts can be performed and only onedifferent partial data has to be recovered, the parities B1(i) and C1(j)or the parities B2(i) and C2(j) may be used as the parity information.One advantage of using only the latter parities B2(i) and C2(j) is thatif two partial data A(i,j) are exchanged in a column or row, forexample, the position of the difference between two sequences can bedetected.

If up to two different partial data A(i,j) have only to be recovered foreach column and each row, any two selected from parities B1(i), B2(i),B3(i) and any two selected from parities C1(j), C2(j), C3(j) may be used(computed) as the first and second sets of parity information,respectively. Furthermore, if the numbers of the different partial datato be recovered of each column and of each row may be different fromeach other, the numbers of the parities of the first and second sets ofparity information may be different from each other. In addition, morethan or equal to four different partial data have to be recoveredcorrectly for each column and each row, for example, the parity Bs(i)(s=4, 5, . . . ) expressed as Σα^(s(j−1))·A(i,j) and the parity Ct(j)(t=4, 5, . . . ) expressed as Σα^(t(i−1))·A(i,j) have only to becomputed, respectively.

Suppose that the partial data A(i,j) in FIG. 8 are arranged in 64columns and 128 rows, then in order to recover up to three differentpartial data for each column and each row using parities B1(i) to B3(i)and C1(j) to C3(j), each of which is a 128-bit (16-byte) quantity, asshown in FIG. 8, the amount of data of all parity information needs tobe 576·16(=(64+128)·3·16) bytes. On the other hand, the amount of dataof all partial data A(i,j) is 8192·16(=64·128·16) bytes. The total dataof all parity information is thus reduced to almost {fraction (1/14)} ofthat of all the partial data A(i,j).

In the subsequent step 107 in FIG. 4, the information processor 10records the information on the name of the standard sample E, the numberNA1, the binary data BN1, and the parities B1(i) to B3(i), C1(j) toC3(j) in the working file 20 defined in the magnetic disk unit 17. Inthis case, the working file 20 may be divided into two or more files,and the binary data BN1 and the parities B1(i) to B3(i), C1(j) to C3(j)may be recorded in different files. The message digest AB1 computed instep 102 may be recorded in the working file 20 as well as the binarydata BN1.

When the size of the binary data BN1 is large, the binary data BN1 maybe divided into two or more parts, which may be recorded in pluralfiles. In addition, when the size of the text data TX1 in FIG. 7(therefore, the binary data BN1 in FIG. 8) is considerably large, thetext data TX1 may be divided into two or more data groups of about 100KB, and the parities B1(i) to B3(i), C1(j) to C3(j) may be computed foreach data group.

Furthermore, also in step 107, the information recorded in the workingfile 20, i.e. the information on the name of the standard sample E, thenumber NA1, the binary data BN1, and the parities B1(i) to B3(i), C1(j)to C3(j), and the information on the massage digest AB1, ABR1 recordedin the master file 19 may be recorded in the CD-R 16 by means of theCD-R/RW drive 15 under the control of the supplier of DNA information.In addition, the supplier may reproduce the CD-R 16 on many CD-ROMs, andsell these recording mediums to users by mail and the like.

Then, in step 108, the information processor 10 records the informationon the name of the standard sample E, the number NA1, the sequences ST1and SB1, the message digest AB1, the reversed sequences STR1 and SBR1,and the message digest ABR1 of the reversed sequence in a contents file21 defined in the magnetic disk unit 17. Even if the size of the textdata TX1 in FIG. 7 is as large as about 100 MB, the size of the datarecorded in the contents file 21 is as small as about 500 bytes. Theinformation processor 10 then transmits the information recorded in thecontents file 21 to the contents provider 3 through the communicationsnetwork 1. Consequently, the information in the contents file 21 isrecorded in the contents file 31, which is defined in the server of theprovider 3 and is freely accessible, and the information in the contentsfile 21 has become disclosed to the public via the Internet.

In the next step 109, the supplier of DNA information enters the stateto wait for purchase orders from users. When, as a case (a), a usersends a purchase order for the summary data of the standard sample E,the procedure moves to step 110, and the information processor 10transmits the parity information (parities B1(i) to B3(i), C1(j) toC3(j)) in the working file 20 defined in the magnetic disk unit 17 tothe user as an email attachment, for example. On the other hand, when,as a case (b) in step 109, a user sends a purchase order for thecomplete data, the procedure moves to step 111. Here the informationprocessor 10 compresses the binary data BN1 in the working file 20 intothe data such as a ZIP file and the like, and transmits the compresseddata to the user as an email attachment, for example. In this case (b),the information processor 10 may transmit the message digest AB1computed by the hash function as well, if necessary. According to thisembodiment, since the size of the summary data (the parity information)is small, the summary data can be transmitted in a short time.

Also in step 109, the user may purchase only part of all data, i.e.necessary data (for example, only the two partial data A(4,16) andA(1,17)) selected from all the partial data A(i,j) in FIG. 8 from thesupplier, if necessary. Hence only necessary and accurate data can bepurchased in a short time.

Then, in step 121 in FIG. 5, the user of DNA information (the owner ofthe computer system 2B in FIG. 1) accesses the contents file 31 in theserver of the provider 3 through the communications network 1 (theinternet) in FIG. 1. The user then reads the information transmitted bythe supplier in step 108, i.e. the information on the name of thestandard sample E, the number NA1 of nucleotides, the sequences ST1 andSB1, the message digest AB1, the reversed sequences STR1 and SBR1, andthe message digest ABR1 of the reversed sequence from the contents file31, and the user records the just-read information in the temporary filedefined in a memory device of the computer system 2B.

In the subsequent step 122, the user reads the sequence of nucleotidesof one chain of the DNA of the sample F under inspection by means of aDNA sequencer (not shown), where the sample F is of the same type as thestandard sample E. The user then transfers the text data TX2 (which isassumed to be expressed in ASCII codes) representing the just-decodedsequence to the information processor of the computer system 2B. Thesample F under inspection is, for example, an E. coli that seems to havemutated, and the text data TX2 is supposed to represent the sequence ofthe first 2048 nucleotides in the same way as the text data TX1 of thestandard sample E.

The DNA sequence of the sample F is shown in SEQ ID NO:2 in SequenceListing. The text data shown in FIG. 9 described below was generated byremoving all numerical data from the sequence in SEQ ID NO:2 andreplacing the characters a, g, c, and t respectively by the charactersA, G, C, and T in the sequence.

FIG. 9 shows the text data TX2 corresponding to the nucleotide sequenceof the DNA of the sample F; and only the underlined portions of thesequence shown in FIG. 9 are different from the sequence of the standardsample E shown in FIG. 7. That is, of the sequence of the sample F onlythe portions corresponding to the partial text data T(4,16) and T(1,17)of the standard sample E are different as follows. At this stage, it isnot known to the user which part of the sequence of the sample F isdifferent from that of the standard sample E. the standard sample E thesample F T(4, 16) = ATTTGGACGGACGTTG → ATTTGGACATTATGGC T(1, 17) =ACGGGGTCTATACCTG → GGCCAACTTATACCTG

Now, the application program to process sequence information on DNA isstarted in the information processor of the user's computer system 2B.Then, in step 123, the information processor computes the 128-bitmessage digest AB2 by applying the above-mentioned MD5 hash function tothe just decoded text data TX2. The information processor also obtainsthe number NA2 of nucleotides of the sequence and two 8-characternucleotide sequences ST2 and SB2 corresponding respectively to the topand end portions of the sequence, and records these data in the firstdata file defined in a built-in storage device. These valuescorresponding to the text data TX2 (FIG. 9) are as follows:AB 2=hex(1457b51222a83c3222e87cb4d4e63305),   (25)NA2=2048,ST2=AGCTTTTC, SB2=CGCGAAGG.

In the next step 124, the information processor checks whether thenumber NA2 of the sample F and the number NA1 of the standard sample Eare equal, and if they are different, the procedure of the user moves tostep 125, and the user retrieves another DNA information to find out theDNA information on the sequences each having nucleotides that amount tothe same number as NA2. In this embodiment, since NA2=NA1 in step 124,the procedure moves to step 126, and the information processor checkswhether the sequences ST2 and SB2 of the top and end portions of thesample F are equal to the sequences ST1 and SB1 of the standard sample Erespectively. The information processor also checks whether the messagedigest AB2 of the sample F is equal to the message digest AB1 of thestandard sample E (which is recorded in the temporary file in step 121).If both checks are affirmative, it is affirmative in extremely highprobability (the error rate is nearly ½¹²⁸≈{fraction (1/10)}³⁸) that thesequence of the sample F matches the sequence of the standard sample E.In this case, the procedure moves to step 127, and the informationprocessor of the computer system 2B records the information indicatingthat “the DNA structure of the sample F is the same as that of thestandard sample E” in the first data file.

However, in this embodiment, although it is satisfied that ST2=ST1 andSB2=SB1, it is clear that AB2≠AB1 from equations (11) and (25). Theprocedure thus moves from step 126 to step 128, and the informationprocessor checks whether the sequences ST2 and SB2 of the top and endportions of the sample F are equal to the sequences STR1 and SBR1 of thereversed sequence of the standard sample E respectively. The informationprocessor also checks whether the message digest AB2 of the sample F isequal to the message digest ABR1 of the reversed sequence of thestandard sample E. If both checks are affirmative, it is considered inextremely high probability that the sequence of the sample F matches thereversed sequence of the standard sample E. In this case, the proceduremoves to step 139, and the information processor of the computer system2B records the information indicating that “the DNA structure of thesample F is related to that of the standard sample E in such a way thatthey are palindromes to each other” in the first data file.

In this embodiment, since ST2≠STR2, SB2≠SBR2, and it is clear thatAB2≠ABR1 from equations (12) and (25), the procedure moves from step 128to step 129. Here the user purchases the above-mentioned summary data,i.e. the parity information (B1(i) to B3(i), C1(j) to C3(j)) of thestandard sample E (the information shown in FIG. 8) from the supplier ofDNA information through the communications network 1 (the internet), andthe user records the purchased information in the second data filedefined in the memory unit of the computer system 2B (the informationprocessor).

Then, in step 130 in FIG. 6, the information processor of the computersystem 2B divides the text data TX2 of the sample F into plural16-character partial text data TF(i,j) (i=1 to N, j=1 to M) arranged inN columns in the arranged direction (corresponding to the directionalong which nucleotides are placed) and in M rows in the non-arrangeddirection as shown in FIG. 9. The numbers N and M of division are thesame as those of the standard sample E, and it is supposed that N=4,M=32 in this embodiment. In addition, the information processor convertseach partial text data TF(i,j) in FIG. 9 into the partial data AF(i,j)consisting of 128(=16·8)-bit binary data (numerical data) using thefollowing function asc(TF(i,j)), which simply converts the text datainto the ASCII codes. In this case, the characters corresponding to thepartial text data TF(i,j) are also converted to a string of ASCII codesin reversed order.AF(i,j)=asc(TF(i,j))   (26)

The partial data AF(i,j) arranged in 4 columns and 32 rows are thusobtained as shown in FIG. 10. A set of data (the numerical data)obtained by arranging all of the partial data AF(i,j) consecutively arereferred to as the binary data BN2.

In the same way as the procedure of step 106, the information processorthen computes the first parity B1F(i), the second parity B2F(i), and thethird parity B3F(i) for the partial data AF(i,j) of each column (i=1 to4) shown in FIG. 10 by adding up all the partial data AF(i,j),calculating the sum Σα^((j−1))·AF(i,j), and calculating the sumΣα^(2(j−1))·AF(i,j), respectively, along the non-arranged direction (j=1to 32) of each column on Galois field GF(2¹²⁸). These parities B1F(i) toB3F(i) in the non-arranged direction (the first set of parityinformation) are computed using the primitive element α of equation (15)and by performing the operations similar to equations (19) to (21)modulo the irreducible polynomial GF(X) for the range 1 to 4 of i.

The information processor then computes the first parity C1F(j), thesecond parity C2F(j), and the third parity C3F(j) for the partial dataAF(i,j) of each row (j=1 to 32) shown in FIG. 10 by adding up all thepartial data AF(i,j), calculating the sum Σα^((i−1))·AF(i,j), andcalculating the sum Σα^(2(i−1))·AF(i,j), respectively, along thearranged direction (i=1 to 4) of each row on Galois field GF(2¹²⁸).These parities C1F(j) to C3F(j) in the arranged direction (the secondset of parity information) are computed using the primitive element α ofequation (15) and by performing the operations similar to equations (22)to (24) modulo the irreducible polynomial GF(X) for the range 1 to 32 ofj.

The parities B1F(i) to B3F(i) and C1F(j) to C3F(j) actually computed byusing the partial data AF(i,j) are shown in vector representation ofhexadecimal notation in FIG. 10.

In the next step 131, the information processor compares the two sets ofparities in the summary data purchased from the supplier, i.e. two setsof parities B1(i) to B3(i) and C1(j) to C3(j) in FIG. 8 (of the standardsample E) with two sets of parities B1F(i) to B3F(i) and C1F(j) toC3F(j) in FIG. 10 (of the sample F), and the information processorsearches them for the differences. According to this embodiment, theparities B1F(1) to B3F(1), B1F(4) to B3F(4) (i=1,4) in the non-arrangeddirection and the parities C1F(16) to C3F(16), C1F(17) to C3F(17)(j=16,17) in the arranged direction in FIG. 10 (of the sample F) aredifferent from the counterparts in FIG. 8 (of the standard sample E). Ifat least one of the parities B1F(i) to B3F(i) in a column or theparities C1F(j) to C3F(j) in a row is different from the counterpart,the parities in the column or the row are considered to be differentfrom the counterparts as a whole, respectively.

Consequently, of all the partial data AF(i,j) in FIG. 10 (of the sampleF), the four partial data AF(1,16), AF(4,16), AF(1,17), and AF(4,17),which are located in the points where the columns with i=1, 4 and therows with j=16, 17 intersect, can be identified as being different fromthe counterparts in FIG. 8 (of the standard sample E). Furthermore, thepartial data AF(i,j) of the sample F other than those different ones canbe considered to be almost the same as the counterparts of the partialdata A(i,j) of the standard sample E.

FIG. 11 shows mainly the parities B1F(1) to B3F(1), B1F(4) to B3F(4),C1F(16) to C3F(16), and C1F(17) to C3F(17) of the sample F in FIG. 10differing from the counterparts in FIG. 8. The data X1, X2, Y1, and Y2to be recovered are also indicated in FIG. 11 at the positions ofpartial data AF(1,16), AF(4,16), AF(1,17), and AF(4,17) differing fromthe counterparts in FIG. 8. These data X1, X2, Y1, and Y2 to berecovered are identical to the partial data A(1,16), A(4,16), A(1,17),and A(4,17), respectively, in FIG. 8 (the standard sample E).

In the next step 132, the information processor checks whether thenumber of the partial data (hereinafter referred to as “AF(i′,j′)”),which differ from the counterparts of the partial data A(i,j) in FIG. 8,of the partial data AF(i,j) in FIG. 10 is three at the most for eachcolumn and each row. If the result of the check is affirmative, thepartial data of the standard sample E corresponding to the partial dataAF(i′,j′) can be computed (recovered) correctly by solving simultaneousequations on Galois field GF(2¹²⁸). In this embodiment, since the numberof the partial data differing from the counterparts is two for 1stand4th columns and two for 16th and 17th rows, the result of the check isaffirmative. The procedure thus moves to step 133, and the informationprocessor recovers the corresponding partial data A(i′,j′) (X1, X2, Y1,Y2) of the standard sample E in accordance with the flowchart of FIG. 12using two sets of different parities and the partial data of the sampleF differing from the counterparts. All the computations in FIG. 12 arecarried out on Galois field GF(2¹²⁸).

In this case, since the number of the unknown numbers X1, X2 in the 16throw is two in FIG. 11, simultaneous first-degree equations with twovariables are formed using two parities C1F(16), C2F(16) in the 16throw, the corresponding two parities C1(16), C2(16) in FIG. 8, and thepartial data AF(1,16), AF(4,16) of the sample F corresponding to theunknown numbers X1, X2. That is, the equations for the parities C1(16)and C1F(16) reduce to equations (G1) and (G2) of step 141 in FIG. 12,and the equations for the parities C2(16) and C2F(16) reduce toequations (G3) and (G4) of step 142 using the primitive element α ofequation (15).

Equations (G5) and (G6) of step 143 are then obtained by subtracting theequations (G2) and (G4) from the equations (G1) and (G3), respectively.The simultaneous first-degree equations with two variables are thenobtained by assuming the right sides of the equations (G5) and (G6) tobe C1X and C2X respectively. Then, the unknown numbers X1 and X2 can beexpressed in equations (G7) of step 144 by solving the simultaneousequations. Actually solving the equations gives the values of X1 and X2as follows (see FIG. 11). It should be noted that if the number of theunknown numbers is 3, simultaneous first-degree equations with threevariables have only to be solved, for example, further using the thirdparities C3(16), C3F(16). If the number of the unknown is 1, theequations can be solved using only the first parities C1(16), C1F(16)and the like.X 1=hex(43475447474347544347544354434154)   (27)X 2=hex(47545447434147474341474754545441)   (28)

In addition, these numerical data are converted to the sequences ofcharacters as follows using a function chr( ) which converts a string ofASCII codes to a string of characters (see FIG. 11). In contrast to theabove-mentioned function asc( ), the function chr( ) converts a stringof ASCII codes to a string of characters one byte by one byte so thatthe most significant and the least significant ASCII codes are convertedto characters placed at the end and front parts, respectively. chr(X1) =TACTCTGCTGCGGTGC = T(1, 16) = (29) TF(1, 16) chr(X2) = ATTTGGACGGACGTTG= T(4, 16) (30)

Thus, it is understood that the partial text data T(1,16) of thestandard sample E is the same as the partial text data TF(1,16) of thesample F, and only the partial text data T(4,16) is different from thepartial text data TF(4,16) (see FIG. 9).

Then, regarding the unknown numbers Y1, Y2 in the 17th row in FIG. 11,simultaneous first-degree equations with two variables are formed usingtwo parities C1F(17), C2F(17) in the 17th row, the corresponding twoparities C1(17), C2(17) in FIG. 8, and the partial data AF(1,17),AF(4,17) of the sample F corresponding to the unknown numbers Y1, Y2.The simultaneous first-degree equations consist of equations (G8) and(G9) of step 145 in FIG. 12. Then, the unknown numbers Y1 and Y2 can beexpressed in equations (G10) of step 146 by solving the simultaneousequations. Actually solving the equations gives the values of Y1 and Y2as follows (see FIG. 11):Y 1=hex(47544343415441544354474747474341),   (31)Y 2=hex(41544343544754414743544741414754).   (32)

These numerical data (a string of ASCII codes) are further converted tostrings of characters as follows (see FIG. 11): chr(Y1) =ACGGGGTCTATACCTG = T(1, 17), (33) chr(Y2) = TGAAGTCGATGTCCTA = T(4, 17)= (34) TF(4, 17).

Thus, it is understood that the partial text data T(4,17) of thestandard sample E is the same as the partial text data TF(4,17) of thesample F, and only the partial text data T(1,17) is different from thepartial text data TF(1,17) (see FIG. 9). According to the method of thisembodiment, the unknown numbers X1, X2, Y1, and Y2, i.e. the partialdata A(1,16), A(4,16), A(1,17), and A(4,17) of the standard sample E arerecovered correctly. Here, since the partial data A(1,16) and A(4,17)are the same as the partial data AF(1,16) and AF(4,17), respectively,those partial data need not be considered as the recovered data.

In the next step 134, after substituting the recovered partial dataA(i′,j′), i.e. A(4,16) and A(1,17) for the corresponding partial dataAF(4,16) and AF(1,17) of the binary data BN2 of the sample F in FIG. 10,the information processor inversely converts the binary data BN2obtained by the substitution into the text data TX1′. In addition, theinformation processor computes the 128-bit message digest AB1′ of thetext data TX1′ by the MD5 hash function, and checks whether the messagedigest AB1′ is equal to the message digest AB1 (which is recorded in thetemporary file in step 121) of the standard sample E. In thisembodiment, it holds true that AB1′=AB1. However, there is somepossibility that the positions of the partial data AF(i,j) of the sampleF in FIG. 10 differing from the counterparts cannot be detectedcorrectly, depending on where and how the partial data differing fromthe counterparts are distributed. If this is the case and it holds truethat AB1′≠AB1, the procedure only has to move to step 135. Since inusual cases it holds true that AB1′=AB1, the procedure moves to step138, and the information processor records the information on “thepositions (i′,j′) of the differences between the sequences of the sampleF and the standard sample E and the pairs of the differing partial textdata” in the above-mentioned first data file. In this embodiment, thepositions (4,16) and (1,17) are recorded as the positions (i′,j′) andthe partial text data A(4,16), AF(4,16), and A(1,17), AF(1,17) arerecorded as the pairs of the differing partial text data.

On the other hand, in step 132, if the number of the partial dataAF(i′,j′) differing from the counterparts is four or more at least forone column or one row, then the correct recovery of the partial data inthe column or the row is difficult, respectively. The procedure thusmoves to step 135, and the user purchases the complete data of thestandard sample E, i.e. the binary data BN1 in FIG. 8 from the supplierof the DNA information through the communications network 1 (theInternet), and the information processor of the computer system 2Brecords the binary data BN1 in the third data file defined in the memorydevice.

Then, in step 136, the information processor inversely converts thebinary data BN1 into the text data TX1′, and computes the 128-bitmessage digest AB1′ by applying the MD5 hash function to the text dataTX1′. The information processor then checks whether the message digestAB1′ is equal to the message digest AB1 of the standard sample E (whichis recorded in the temporary file in step 121). In usual cases it holdstrue that AB1′=AB1, but if the binary data BN1 is not transmittedcorrectly because of communication errors, for example, it follows thatAB1′≠AB1. In this case, for example, the information processor requeststhat the supplier transmit the complete data again. If it holds truethat AB1′=AB1 in step 136, the procedure moves to step 137, and theinformation processor obtains the partial data A(i′,j′), whichcorrespond to the different partial data AF(i′,j′) of the sample F, ofthe binary data BN1 of the standard sample E. The procedure then movesto step 138.

In the above-mentioned step 135, the user purchases the complete data(the binary data BN1) from the supplier of DNA information. However,instead of the procedure in the step 135, the user may purchase only thepartial data A(i′,j′), which is identified in the step 131 andcorresponds to the different partial data AF(i′,j′) of the standardsample E. This reduces the communications cost.

According to the business model of this embodiment of the invention, atthe first stage, the parity information of the standard sample E (B1(i)to B3(i), C1(j) to C3(j)) is purchased. Then, the purchased parityinformation and the parity information of the sample F (B1F(i) toB3F(i), C1F(j) to C3F(j)) are compared. And, if the number of thedifferent partial data AF(i,j) is small, the corresponding partial dataA(i,j) of the standard sample E is recovered, while if the number of thedifferent partial data is large, the complete data or only the differentpartial data is purchased. The user thus doesn't need to purchase a hugeamount of the complete data at first, and the communications time can beshortened and the cost needed for information processing can be reduced.

Furthermore, by using the parity information of this embodiment of theinvention, the error such as the SNP (Single Nucleotide Polymorphism) inwhich only one nucleotide (or base) differs from the counterpart withina certain range can be easily detected and correctly recovered.

In the above-stated embodiment, the user of the DNA information readsthe sequences ST1, SB1, the message digest AB1, the sequences STR1,SBR1, and the message digest ABR1 of the standard sample E from thecontents file in step 121. The user then checks whether the standardsample E and the sample F are the same in steps 122-128, and if the twosamples are different, the user purchases the parity information of thestandard sample E (the summary data). However, since it is reasonablethat at least some parts of the sample F are usually different from thecounterparts of the standard sample E, the user may omit the proceduresfrom the acquisition of the message digest AB1, etc. to the check of thesameness of two samples. The user then may purchase the parityinformation of the standard sample E (the summary data) from thesupplier of DNA information by directly performing the procedure of step129.

In the above-stated embodiment, as shown in FIG. 8, the number of thefirst set of parity information (B1(i) to B3(i)) and the number of thesecond set of parity information (C1(j) to C3(j)) are the same. However,when the number (=4) of the partial data A(i,j) in the arrangeddirection is smaller than the number (=32) of the partial data A(i,j) inthe non-arranged direction, the amount of the second set of parityinformation may be made less than that of the first set of parityinformation, for example, by using only C1(j), only C2(j), or only C1(j)and C2(j) as the parity information in the arranged direction. Theamount of data of all the parity information can thus be reduced. Inthis case, any differences between the standard sample E and the sampleF can be accurately detected, and the partial differences like the SNPcan be accurately recovered.

Furthermore, when the number of the partial data placed in the arrangeddirection is smaller than that of the partial data placed in thenon-arranged direction as shown in FIG. 8 (FIG. 7), the partial dataA(i,j) and the parity information can be displayed on a monitorefficiently by letting the arranged direction of the partial data beingparallel (horizontally) to the width of the monitor and scrolling thedisplayed information to the non-arranged direction. In this case,provided that the partial data A(i,j) is an m-bit quantity, the numberof the partial data in the non-arranged direction is preferably smallerthan or equal to (2^(m−)1)/4. Accordingly, since mutually different fourparities can be computed as the parity information in the non-arrangeddirection, ordinary partial differences between two samples can berecovered correctly.

In the above-stated embodiment, the text data TX1 of the standard sampleE in FIG. 7 is converted into the sequence of the partial data A(i,j) inFIG. 8 in step 105, where the size of the text data TX1 is the same ofthat of all the partial data, and the parity information is computedfrom the sequence. Instead of the procedure, in order to reduce theamount of data, the text data TX1 of the standard sample E in FIG. 7 maybe converted into the binary data (numerical data) based on the Table 1(a conversion table representing each nucleotide by two-bit data), wherethe size of the binary data is reduced to ¼ of that of the text data,and the binary data may be divided into the sequence of plural partialdata placed in the arranged direction and in the non-arranged direction.

FIG. 13 shows the sequence of the 64-bit (8-byte) partial data B(i,j)(i=1 to 5, j=1 to 13) obtained like that and arranged in 5 columns inthe arranged direction along which nucleotides are placed and in 13 rowsin the non-arranged direction in hexadecimal notation. Each partial dataB(i,j) in FIG. 13 corresponds to each sequence of consecutive 32nucleotides of the standard sample E in FIG. 7. In the sequence, sincethe part of the standard sample E in FIG. 7 corresponding to the lastpartial data B(5,13) doesn't exist, the dummy data consisting of hex(000. . . 000)) is added to the place of the partial data B(5,13).

Then, in the procedure corresponding to the step 106, a certainoperation on Galois field GF(264) (m=64) is applied to the partial dataB(i,j) by considering the partial data B(i,j) to be an element of Galoisfield GF(2⁶⁴) in vector representation. The following polynomials areused as an irreducible polynomial GF(X) and a primitive element α onGalois field GF(2⁶⁴).GF(X)=1+X ⁵ +X ²³ +X ⁴³ +X ⁶⁴   (35)α′=X   (36)

Moreover, the following irreducible polynomial GF′(X) can also be used,for example, as another irreducible polynomial on Galois field GF(2⁶⁴),and the following element α′ can be used as a primitive elementcorresponding to the irreducible polynomial GF′(X).GF′(X)=1+X ⁷ +X ⁶²+X⁶³ +X ⁶⁴   (35A)α′=1+X   (36A)

The information processor 10 in FIG. 10 then computes the first parityB1B(i), the second parity B2B(i), and the third parity B3B(i) for thepartial data B(i,j) of each column (i=1 to 5) shown in FIG. 13 by addingup all the partial data B(i,j), calculating the sum Σα^((j−1))·B(i,j),and calculating the sum Σα^(2(j−1))·B(i,j), respectively, along thenon-arranged direction (]=1 to 13) of each column on Galois fieldGF(26⁴). These calculations correspond to equations (19) to (21), andeach of the first set of parity information (B1B(i) to B3B(i)) is a64-bit quantity.

In addition, the information processor 10 computes the first parityC1B(j), the second parity C2B(j), and the third parity C3B(j) for thepartial data B(i,j) of each row (j=1 to 13) shown in FIG. 13 by addingup all the partial data B(i,j), calculating the sum Σα^((i−1))·B(i,j),and calculating the sum Σα^(2(i−1))·B(i,j), respectively, along thearranged direction (i=1 to 5) of each row on Galois field GF(2⁶⁴). Thesecalculations correspond to equations (22) to (24), and each of thesecond set of parity information (C1B(j) to C3B(j)) is a 64-bitquantity.

In this case, the amount of data of the two sets of parity information(B1B(i) to B3B(i), C1B(j) to C3B(j)) can be reduced to almost ¼ of thatof the parity information (B1(i) to B3(i), C1(j) to C3(j)) in FIG. 8.Thus, the parity information can be transmitted in a short time throughthe communications network and the information can be recorded inmediums whose memory capacity is relatively small.

In this case, when the user computes the parity information of thesample F in FIG. 9, the user has only to convert the text data of thesample F to the partial data based on the Table 1, where the size of allthe partial data is reduced to ¼ of that of the text data, and computethe first and second sets of parity information by performing theoperations on Galois field GF(2⁶⁴). Then, the detection of the positionsof the different data and the recovery of the data of the standardsample can be carried out in a similar manner to the above-statedembodiment. 5 In the above-stated embodiment, since there are four kindsof nucleotides constituting DNA or RNA, when the text data TX1 isconverted into the reduced binary data, each nucleotide is representedby two-bit data as shown in Table 1. On the other hand, in someapplications the following 16 kinds of characters a-n (8-bit ASCII code)are used as the text data showing each nucleotide (or base). TABLE 2 Aadenine (this indicates the nucleotide including adenine, and so forth)c cytosine g guanine t thymine u uracil m adenine or cytosine r guanineor adenine w adenine or thymine (or uracil) s guanine or cytosine ythymine (or uracil) or cytosine k guanine or thymine (or uracil) vadenine, guanine, or cytosine h adenine, cytosine, or thymine (oruracil) d adenine, guanine, or thymine (or uracil) b guanine, cytosine,or thymine (or uracil) n (adenine, cytosine, guanine, or thymine (oruracil)) or (unknown or other base)

In this case, these 16 kinds of characters may be converted intomutually different four-bit codes, and then the text data may beconverted into the numerical data (binary data) using the four-bitcodes. This conversion reduces the amount of data by half Furthermore,if the kinds of nucleotides (bases) increase in the future, thenucleotides may be expressed as the data of five or six bits.

Although in the above-mentioned embodiment the messages digests arecomputed by applying the hash function to the text data showing thenucleotide sequences in FIGS. 7 and 9, those text data are equivalent tothe binary data (numerical data) converted based on Table 1, forexample, in terms of the amount of the sequence information. Therefore,the message digests may be computed by applying the hash function to thebinary data so as to be compared. Since the size of the binary data isnearly one-fourth of the size of the text data, the computation time forthe message digest can be shortened.

In the above-stated embodiment, the information on the sequences ofnucleotides (or the sequences of bases) constituting DNA or RNA isprocessed. However, the present invention can also be applied to thecases in which the information on sequences of nucleotides constitutinggenes is processed.

Another embodiment of the present invention will be described next withreference to the accompanying drawings. In this embodiment of theinvention, some pieces of information on sequences of amino acids(biological compounds) in proteins or peptides are processed withcomputer systems.

In this embodiment, the computer system 2A shown in FIG. 1 can also beused basically, except that a protein sequencer is connected to theinformation processor 10 as the sequencer for reading amino acidsequences in proteins instead of the sequencer 4 for DNA. It should benoted that databases of amino acid sequences can also be used as theprotein sequencer. In this embodiment, suppose that the sequence ofamino acids in the protein of the newly discovered sample G, forexample, is read by the sequencer, and the text data (hereinafterreferred to as “TX3”) showing the sequence is supplied to theinformation processor 10. The size of the text data corresponding to thesequence of n amino acids is n bytes, provided that one-Letter Code isused. In this embodiment, the sample G is supposed to be E. coli, whosesequence data was obtained from the above-mentioned website 1. The textdata showing the sequence of a series of 820 amino acids in a certainprotein of E. coli is used as the text data TX3 as shown in FIG. 14.

The sequence of a series of amino acids in the sample G is shown in SEQID NO:3 in Sequence Listing. The text data shown in FIG. 14 wasgenerated by removing all numerical data from the sequence in SEQ IDNO:3 and expressing the sequence in one-Letter Code. Referring to FIG.14, the text data is divided into plural 4-character partial text dataarranged in 8 columns in the arranged direction (corresponding to thedirection along which amino acids are placed) and in 26 rows in thenon-arranged direction normal to the arranged direction, and a series ofdummy “0” are temporarily written in the positions of data showing the821st and later amino acids (this part is not included in the text dataTX3 to be exact).

The information processor 10 then computes the 128-bit message digestAB3 by applying the MD5 hash function to the supplied text data TX3, andobtains the number NA3 of amino acids in the sequence and two sequencesST3 and SB3 of 8 amino acids taken respectively from the top and endportions of the text data TX3 as follows:AB 3=hex(0f66dc2b3024a9739d0e912fde12b8ba),   (41)NA3=820,ST3=MRVLKFGG, SB3=TLSWKLGV.

The information processor 10 then obtains the text data TXR3(=VGLKWS . .. FKLVRM) by rearranging the text data TX3 in reverse order. Inaddition, the information processor 10 obtains the message digest ABR3by applying the MD5 hash function to the text data TXR3, and obtains twosequences STR3 and SBR3 of 8 amino acids corresponding respectively tothe top and end portions of the text data TXR3. The sequences STR3 andSBR3 are easily obtained by rearranging the sequences SB3 and ST3 inreverse order. These values are as follows. It may be said that thesequence of the text data TXR3 is related to that of the original textdata TX3 in such a way that they are palindromes to each other.ABR 3=hex(e895f433e1e77f84b3cadeead1a52380)   (42)STR3=VGLKWSLT, SBR3=GGFKLVRM

The information processor 10 subsequently records the information on thename of the sample G (the information identifying the sample), thenumber NA3, the text data TX3, the sequences ST3 and SB3, the messagedigest AB3, the reversed sequences STR3 and SBR3, and the message digestABR3 of the reversed sequence in the master file 19 defined in themagnetic disk unit 17. In this procedure, provided that the master file19 is divided into two or more files, the text data TX3 and other datamay be recorded in different files. The information processor 10 thendivides the text data TX3 of the sample G into partial text data TG(i,j)with eight characters (64-bit data) arranged in N columns in thearranged direction (corresponding to the direction along which aminoacids are placed) and in M rows in the non-arranged direction normal tothe arranged direction as shown in FIG. 14 the same as in FIG. 7, forexample. N and M are arbitrary integers of two or more respectively. Inthis embodiment, the text data TX3′ of 832(=8·4·26) bytes is obtained byadding the dummy data of 12 characters (for example the character “A”may be used as well as the number “0” of this embodiment) to the textdata TX3, and the text data TX3′ is divided such that N=4 and M=26.

In this embodiment, each of the partial text data TG(i,j) with 8characters is treated as just the 64-bit partial data AG(i,j) using thefunction asc( ) which simply converts the text data into the ASCII codes(numerical data) as follows:AG(i,j)=asc(TG(i,j)).   (43)

It should be noted that the function asc(TG(i,j)) converts the partialtext data TG(i,j) in reversed order so that the codes of the charactersat the front and end of the partial text data are placed in the leastand most significant parts, respectively, as shown by the convertedexample of TG(3,11) in FIG. 14. In this case, it is possible to expresseach amino acid as 6-bit data. However, since the amount of data isreduced to only about ¾ of that of the ASCII-code expression, thepartial text data (a string of ASCII codes) is used simply as thepartial data (numerical data) in this embodiment.

FIG. 15 shows the sequence of the partial data AG(i,j) of the sample G.Then, in the same way as the example of FIG. 13, the informationprocessor 10 applies a certain operation on Galois field GF(2⁶⁴) (m=64)to the partial data AG(i,j) by considering the 64-bit partial dataAG(i,j) arranged in 4 columns and 26 rows in FIG. 15 to be elements ofGalois field GF(2⁶⁴) in vector representation. The polynomials definedby equation (35) (or (35A)) and equation (36) (or (36A)) are used as anirreducible polynomial GF(X) and a primitive element α on Galois fieldGF(2⁶⁴), respectively.

More specifically, the information processor 10 computes the firstparity B1G(i), the second parity B2G(i), and the third parity B3G(i) forthe partial data AG(i,j) of each column (i=1 to 4) shown in FIG. 15 byadding up all the partial data AG(i,j), calculating the sumΣα^((j−1))·AG(i,j), and calculating the sum Σα^(2(j−1))·AG(i,j),respectively, along the non-arranged direction (j=1 to 26) of eachcolumn on Galois field GF(2⁶⁴). These calculations correspond toequations (19) to (21), and each of the first set of parity information(B1G(i) to B3G(i)) is a 64-bit quantity.

The information processor 10 then computes the first parity C1G(j), thesecond parity C2G(j), and the third parity C3G(j) for the partial dataAG(i,j) of each row (j=1 to 26) shown in FIG. 15 by adding up all thepartial data AG(i,j), calculating the sum Σα^((i−1))·AG(i,j), andcalculating the sum Σα^(2(i−1))·AG(i,j), respectively, along thearranged direction (i=1 to 4) of each row on Galois field GF(2⁶⁴). Thesecalculations correspond to equations (22) to (24), and each of the firstset of parity information (C1G(j) to C3G(j)) is a 64-bit quantity. Theparities B1G(i) to B3G(i), C1G(j) to C3G(j) computed in this way areexpressed in FIG. 15 in hexadecimal notation.

In this embodiment, three parities are computed for each column and eachrow. However, since the amount of data of an amino acid sequence is muchless than that of a nucleotide sequence, only one parity (for example,B2G(i) and C2G(j)) may be used for each column (in the non-arrangeddirection) and for each row (in the arranged direction) as the parityinformation for practical use. In the embodiment of FIG. 15, supposethat only the parities B2G(i) and C2G(j) are used, then since eachparity is a 64-bit (8-byte) quantity, the data of all parities adds upto 240(=8·30) bytes. The data of all parities is thus reduced to nearly⅓ of that of the original text data TX3 (820 bytes).

Then, the information processor 10 records the information on the sampleG's name, the number NA3, the text data TX3, the message digests AB3,ABR3, and the parity information in the working file 20 defined in themagnetic disk unit 17. The working file 20 may be divided into two ormore files. The information processor 10 then records the information onthe sample G's name, the number NA3, the sequences ST3, SB3, the messagedigest AB3, the reversed sequences STR3, SBR3, and the message digestABR3 of the reversed sequence in the contents file 21 defined in themagnetic disk unit 17. Besides, the information processor 10 transmitsthe information on the data in the contents file 21 to the contentsprovider 3 through the communications network 1, thereby enabling thedata in the contents file 21 to be recorded in the contents file 31defined in the server of the provider 3 and accessible freely. Thismeans that the data in the contents file 21 is disclosed to the publicthrough the Internet. Accordingly, a third party can check whether thesample G is novel to them by comparing the number NA3 and the messagedigest AB3 (or ABR3, if necessary) disclosed to them respectively withthe number of amino acids in the sequence of the sample owned by themand the message digest of the sequence of the sample. In addition, userscan avoids purchasing the same sequence information on the sample G fromtwo or more suppliers by mistake.

Subsequently, the owner of the computer system 2A (the supplier of aminoacid information) enters the state to wait for purchase orders fromusers. When a user sends a purchase order for the summary data of thesample G, the information processor 10 transmits the parity information(for example, B2G(i), C2G(j)) of the sample G in the working file 20defined in the magnetic disk unit 17 to the user as an email attachment.The user who purchased the parity information compares the parities ofthe amino acid sequence of the sample, which is of the same kind as thesample G and which sequence was deciphered by themselves, with thepurchased parities, and thus can detect and recover the differencesbetween the two sequences to some extent.

On the other hand, when a user sends a purchase order for the completedata, the information processor 10 compresses the text data TX3 in theworking file 20 into the data such as a ZIP file and the like, andtransmits the compressed data to the user as an email attachment, forexample. In this case, the information processor 10 may transmit themessage digest AB3 computed by the hash function as well, if necessary.According to this embodiment, since the size of the summary data (theparities) can be reduced, the summary data can be transmitted in a shorttime.

In addition, the supplier of the sequence information on amino acids mayrecord the information stored in the working file 20, i.e. theinformation on the sample G's name, the number NA3, the text data TX3,the message digests AB3, ABR3, and the parity information in the CD-R 16by way of the CD-R/RW drive 15. The CD-R 16 may be reproduced on moreCD-ROMs, and these recording mediums may be sold to users by mail andthe like.

In the above-stated embodiment, the text data corresponding to thesequence of biological compounds or the numerical data obtained byconverting the text data based on a conversion rule is divided intoplural m-bit partial data arranged in plural columns in the arrangeddirection, along which the biological compounds are placed, and inplural rows in the non-arranged direction which crosses the arrangeddirection, where m is an integer larger than or equal to 16. A first setof parity information are then computed by applying a first operation ofGalois field GF(2^(m)) along the non-arranged direction to the partialdata of each column. A second set of parity information are thencomputed by applying a second operation of Galois field GF(2^(m)) alongthe arranged direction to the partial data of each row.

Regarding the procedures, if m is smaller than 16, each partial datacorresponds to the sequence of from 1 to 7 nucleotides or from 1 to 2amino acids, for example. Therefore, there is the inconvenience ofhaving to compute too many pieces of parity information for a sequenceof the biological compounds. In addition, we cannot make the most ofcomputational abilities of resent computers. Especially, when theprocessing unit of computers is a multiple of 64 bits, the value of mmay be preferably a multiple of 64 such as 64, 128, 192, 256, etc. inorder to compute the parity information efficiently.

Moreover, in the embodiment of FIG. 13, provided that the prime numberlarger than m-bit number is denoted by P (P>2^(m)), it is possible tocompute the parity information on Galois field GF(P), in whichoperations are performed mod P. However, since some pieces of the parityinformation obtained by applying operations to the m-bit partial data onGalois field GF(P) exceed m-bit numbers, there is the inconvenience ofhaving the total parity information whose size is (m+1)/m times the sizeof that obtained using Galois field GF(2^(m)). That is, one advantage ofGalois field GF(P) is its easy operations, while one advantage of Galoisfield GF(2^(m)) is its compact parity information, because every pieceof the parity information is expressed as an m-bit number on Galoisfield GF(2^(m)).

In order to seek a large prime number P larger than 2^(m)(m>16) orslightly smaller than 2^(m), for example, the Miller-Rabin's method fortesting primality (see, for example, the reference (M. O. Rabin:“Probabilistic algorithms for testing primality”, Journal of NumberTheory, 12, pp. 128-138 (1980))) can be used. Furthermore, in order tofactorize a large number for seeking a primitive element, for example,the quadratic sieve method (see, for example, the reference (C.Pomerance: “Factoring”, In Cryptology and Computational Number Theory,pp. 27-47, American Mathematical Society (1990))) can be used. Inaddition, a practical method of determining a large prime number P andfactorizing a large number is to use the built-in function “ECM” in theabove-mentioned “UBASIC”.

Galois field GF(P), where P is a prime number, consists of P elements(0, 1, . . . , P−1), and the operations of addition, subtraction,multiplication, and division are carried out mod P on Galois fieldGF(P). In order to apply Galois field GF(P) to the above-statedembodiment of the invention, each of the m-bit partial data A(i,j) hasonly to be expressed as any element of Galois field GF(P). In order tocomputes the parity information easily, a primitive element δ of Galoisfield GF(P) may be used. Provided that k=P−1, the primitive element δ ofGalois field GF(P) satisfies the following relations modulo P:δ^(k)=1(mod P),   (A2)^(k′)≠1(mod P)(1≦k′<k).   (A3)

Suppose that the integer k can be factorized as follows using primenumbers p1, p2, . . . , pr and integers n1, n2, . . . , nr:k=P−1=p1^(n1) ·p2^(n2) . . . pr ^(nr).   (A4)

Then, the primitive element δ is determined so that all of δ to thepower of (p1^(n1−1)·p2^(n2) . . . pr^(nr)), δ to the power of(p1^(n1)·p2^(n2−1) . . . pr^(nr)), . . . and δ to the power of(p1^(n1)·p2^(n2) . . . pr^(nr−1)) do not come to 1 mod P.

Moreover, since an arbitrary nonzero element ε of Galois field GF(P)satisfies equation (A2), the inverse element ε⁻¹ of ε can be computed asfollows by the use of k(=P−1):ε⁻¹=ε^(k−1)(mod P).   (A5)

Therefore, for example, when the partial data is divided by ε, we haveonly to multiply the partial data by ε^(k−1).

Then, when Galois field GF(P) is used, the procedures of the supplierand user of DNA information shown in FIGS. 3 to 6 can be carried out bysubstituting the operations on Galois field GF(P) for the operations onGalois field GF(2^(m)).

More specifically, when the parity information is computed on Galoisfield GF(P) in the embodiment in FIG. 13 (for example, the standardsample), a prime number (for example, the smallest one) that is largerthan 2⁶⁴(m=64) and smaller than or equal to 65(=m+1)-bit numbers may beused as the prime number PF because it is possible that the partial dataB(i,j) will take all 64-bit values. The prime number P of this kind isas follows in hexadecimal notation. In addition, for example, thefollowing number may be used as a primitive element δ corresponding tothe prime number P. In this case, since 3 is also a primitive element,if a number except 2 to the power of any number is preferable as aprimitive element, for example, 3 may be used as the primitive elementδ.P=hex(100000000000000d)   (A6)δ=2   (A7)

In the procedure corresponding to step 106 under these conditions, each64-bit partial data B(i,j) is performed certain operations on Galoisfield GF(P) using the primitive element δ by considering the partialdata B(i,j) to be an element of Galois field GF(P). For example, thefirst parity B1B(i)′, the second parity B2B(i)′, and the third parityB3B(i)′ for the partial data B(i,j) of each column (i=1 to 5) shown inFIG. 13 are computed by adding up all the partial data B(i,j),calculating the sum Σδ^((j−1))·B(i,j), and calculating the sumΣδ^(2(j−1))·B(i,j), respectively, along the non-arranged direction (]=1to 13) of each column on Galois field GF(P). These calculationscorrespond to equations (19) to (21), and each of the first set ofparity information (B1B(i)′ to B3B(i)′) is a (64+1)-bit quantity at themost.

In addition, the first parity C1B(j)′, the second parity C2B(j)′, andthe third parity C3B(j)′ for the partial data B(i,j) of each row (j=1 to13) shown in FIG. 13 are computed by adding up all the partial dataB(i,j), calculating the sum Σδ^((i−1))·B(i,j), and calculating the sumΣδ^(2(i−1))·B(i,j), respectively, along the arranged direction (i=1 to5) of each row on Galois field GF(P). These calculations correspond toequations (22) to (24), and each of the second set of parity information(C1B(j)′ to C3B(j)′) is also a (64+1)-bit quantity at the most.

Furthermore, in the procedure corresponding to step 130, the first andsecond sets of parity information are computed on Galois field GF(P) inthe non-arranged and arranged directions, respectively, for the partialdata sequence of the sample under inspection. Then, in the procedures ofthis embodiment corresponding to steps 131-138, the comparison betweenthe parity information of two samples, the detection of the differentpartial data, and the recovery of the different data can be carried out.

Then, provided that the partial data takes all 128-bit values (m=128),in order to compute the parity information for the partial data onGalois field GF(P), the following prime number may be used as a primenumber P lager than 2¹²⁸ and smaller than or equal to 129-bit number.And, the following number may be used as a primitive element δcorresponding to the prime number P.P=2¹²⁸+51   (A8)δ=2   (A9)

On the other hand, when the text data itself is used as the partial dataA(i,j) like the embodiments of FIGS. 7 and 8, the maximum value Nmax ofthe m-bit partial data A(i,j) is smaller than (2^(m−)1). Morespecifically, suppose that ASCII codes are used as the text data in FIG.7, since the ASCII codes of the alphabets are hex(41) to hex(7a), themaximum value Nmax is as follows:Nmax=hex(7a7a7a7a . . . 7a7a7a)<2^(m)−1.   (A10)

In this case, the prime number P defining the Galois field GF(P) can beselected so that it is not only larger than the maximum value Nmax ofthe partial data A(i,j) but it is also an m-bit number as follows:2^(m)>P>Nmax.   (A11)

Furthermore, when m=128 and the equation (A10) holds good, the smallestprime number P that satisfies the equation (A11) and a primitive elementδ corresponding to it are as follows:P=hex(7a7a7a7a7a7a7a7a7a7a7a7a7a7a7a7f),   (A12)δ=5.   (A13)

When the first and second sets of parity information of the partial dataA(i,j) in FIGS. 7 and 8 are computed on Galois field GF(P) using thisprime number P and this primitive element δ, each parity computed inthis way is an m-bit quantity. Thus, according to this method, theoperations are simple and the compact parity information whose size isthe same as that computed on Galois field GF(2^(m)) is obtained.

Similarly, when ASCII codes are used as the text data in the embodimentin FIGS. 14 and 15, the maximum value Nmax of the m-bit partial dataAG(i,j) (m=64 in the case of FIG. 14) is as follows:Nmax=hex(7a7a7a7a7a7a7a7a)<2^(m)−1.   (A14)

In this case, the prime number P defining the Galois field GF(P) canalso be selected so that the equation (A11) is satisfied.

More specifically, when m=64 and the equation (A14) holds good, thesmallest prime number P that satisfies the equation (A11) and aprimitive element δ corresponding to it are as follows. In this case,since 5 is also a primitive element, for example, if a number except 2to the power of any number is preferable as a primitive element, 5 andthe like may be used as the primitive element δ.P=hex(7a7a7a7a7a7a7ad5)   (A15)δ=2   (A16)

Furthermore, when the parity information is computed on Galois fieldGF(P), the number of the partial data placed in the arranged directionmay be made smaller than that of the partial data placed in thenon-arranged direction, and the number of the second set of parityinformation in the arranged direction may be made smaller than that ofthe first set of parity information in the non-arranged direction.Accordingly, the parity information can be easily displayed on amonitor, and the total amount of data of the parity information is keptfrom growing too much. In this case, in order to recover up to fourdifferent data in the non-arranged direction correctly using theprimitive element δ, the number of the partial data in the non-arrangeddirection has only to be made smaller than or equal to (P−1)/4.

In the above-stated embodiments, the parity information is computed bymultiplying each partial data by a certain coefficient. However, forexample, we may use the BCH codes (Bose-Chaudhari-Hocquenghem Codes)(see, for example, reference (J. L. Massey: “Shift Register Synthesisand BCH Decoding,” IEEE Trans., IT-15, pp. 122-127 (1969))) as theparity information. It should be noted that the conventional BCH codesare constructed on Galois field GF(2^(m′)), where m′ is a small numbermaybe smaller than or equal to 16. Thus, in order to apply the BCH codesto the present invention, the BCH codes have to be reconstructed onGalois field GF(2^(m)), where m is a large number larger than or equalto 16 as is the case with the present invention.

Here, the hash function used in the above-stated embodiments will bedescribed in more detail. The conventional hash function used incryptography processes all codes including space code, linefeed code(return code), etc. in the text data. As for the sequence information onnucleotides and amino acids, as shown in SEQ ID NO:1 to 3 in SequenceListing, space codes, numerical codes showing the order of the sequence,and linefeed codes are sometimes inserted in the text data so that thesequence is easy to read. Therefore, the hash function used forprocessing the sequence information on biological compounds such asnucleotides and amino acids may preferably have the function to leaveout (disregard) the predetermined codes such as numerical codes, spacecode, and linefeed code. In addition, when one or more hyphen codes “-”are inserted between the adjacent characters (letters), the hashfunction needs to further leave out the hyphen codes. Furthermore, if “akind of termination code” is added at the end of a file, the hashfunction may leave out such code.

In addition, if the sequences of nucleotides are usually written, forexample, in lower-case letters, the hash function may compute themessage digest after converting upper-case letters, which are unusuallyused, to lower-case letters selectively. On the contrary, if thesequences of amino acids are usually written, for example, in upper-caseletters, the hash function may compute the message digest afterconverting lower-case letters, which are unusually used, to upper-caseletters selectively.

In addition, when the original file is divided into two or more partialfiles, it might be sometimes preferable to add data (hereinafterreferred to as “comment data”) showing the order of division of thepartial files and the like to each partial file. When the comment datais added to each partial file or one original file, the hash functionneeds to leave out the comment data. In order to leave out the commentdata, for example, after recording the comment data between a certainstart symbol (for example, /*) and a certain end symbol (for example,*/), the hash function has only to leave out the data from the startsymbol to the end symbol.

Furthermore, according to the above-mentioned embodiment, the partialsequences of the first and end parts of the nucleotide sequence in theDNA of an organism (or the amino acid sequence in a protein) and themessage digest of the text data showing the sequence are sometimesdisclosed on the Internet. In this case, there is a possibility that thetext data is recovered from the disclosed partial sequences and themessage digest. When the message digest of the text data is computed,the hash function may be performed on the remainder that is left afterremoving the partial sequences from the text data in order to avoid therecovery.

Then, in the step 124 in FIG. 5 of the above-stated embodiment, if thenumber NA2 of the sample F's sequence differs from the number NA1 of thestandard sample E's sequence by k (k is an integer larger than or equalto 1) and, for example, NA2=NA1+k, the data corresponding to knucleotides may be removed from the text data TX2 of the sample F, andthen the procedure may move to step 126 to search for the differences.On the contrary, if it stands up that NA2=NA1−k, the dummy datacorresponding to k nucleotides may be added to the text data, and thenthe procedure may move to step 126. Accordingly, the positions of theexcesses or deficits of the sample F's sequence can be identified. Inthis case, if k=1, the position in the text data TX2, from which theexcess data is removed or to which the dummy data is added, maypreferably be at first a position dividing the total sequence half-and-half, then a position dividing the first or second half of thesequence half-and-half, then a position dividing the first or secondhalf of the divided sequence, and so on. Accordingly, the position ofthe excess or deficit can be identified in the shortest time.

The present invention has been described above with respect to variouspreferred embodiments. However, the present invention is not limited tothese embodiments. Various changes or modifications may be made withinthe scope of the present invention.

Industrial Applicability

According to the present invention, the sequence information onbiological compounds such as nucleotides in nucleic acids or genes andamino acids in proteins or peptides can be approximately represented bythe parity information. The parity information can then be recorded inless amounts of data than the text data expressing the sequence.Therefore, the parity information can be recorded in mediums whosememory capacity are small and can be transmitted through acommunications network in a short time. In addition, by performingoperations on Galois field GF(2^(m)), each parity information can berecorded concisely in the same amount of data as the m-bit partial data.

On the other hand, when the operations are performed on Galois fieldGF(P), where P is a prime number, in order to compute the parityinformation, the size of the parity information increases to (m+1)/mtimes that computed on Galois field GF(2^(m)), while the operations aresimplified.

Especially, when the maximum value Nmax of the partial data is smallerthan (2^(m−)1) and the prime number P can be selected so that therelation (2^(m)>P>Nmax) is satisfied, the operations are simple and eachpiece of parity information can be recorded concisely in the same amountof data as the m-bit partial data.

Furthermore, the differences between two sequences of biologicalcompounds can be easily identified (detected) by comparing two sets ofparity information of the two sequences. And, the differences can berecovered, if necessary. Accordingly, the SNP (Single NucleotidePolymorphism) can be easily detected by comparing two pieces of smallamounts of data.

Furthermore, according to the present invention, a business model isprovided, in which the parity information that approximately representsthe sequence information on biological compounds such as nucleotides andamino acids can be supplied to uses in small amounts of data. In thiscase, by further using the mathematical digest, the user can easilycheck whether the purchased sequence information and the sequenceinformation owned by the supplier are equal. In addition, the user canavoid purchasing the same sequence information from different suppliersby mistake.

1. Method for recording sequence information on biological compounds,comprising the steps of: dividing one of text data representing asequence of said biological compounds and numerical data obtained byconverting said text data, utilizing a conversion rules into a pluralityof m-bit partial data arranged in a plurality of columns in an arrangeddirection corresponding to a direction along which said biologicalcompounds are placed and in a plurality of rows in a non-arrangeddirection which crosses said arranged direction, where m is an integergreater than or equal to 16; computing a first set of parity informationby applying a first operation of a Galois field GF(2^(m)) along saidnon-arranged direction to a set of said partial data of each column;computing a second set of parity information by applying a secondoperation of a Galois field GF(2^(m)) along said arranged direction to aset of said partial data of each row; and representing said sequenceinformation on said biological compounds by said first and second setsof parity information.
 2. Method of claim 1, wherein when α is aprimitive element of a Galois field GF(2^(m)), said first set of parityinformation includes a sum of a plurality of products obtained bymultiplying a set of said partial data of each column along saidnon-arranged direction by α^(sp), α^(s(p+1)), α^(s(p+2)), . . . ,α^(s(p+dp)), where s and p are nonnegative integers and dp is an integergreater than or equal to one; and said second set of parity informationincludes a sum of a plurality of products obtained by multiplying a setof said partial data of each row along said arranged direction byα^(tq), α^(t(q+1)), α^(t(q+2)), . . . , α^(t(q+dq)), where t and q arenonnegative integers and dq is an integer greater than or equal to one.3. Method of claim 2, wherein a number of said partial data placed alongsaid arranged direction is smaller than a number of said partial dataplaced along said non-arranged direction; and a number of said secondset of parity information is smaller than a number of said first set ofparity information.
 4. Method of claim 3, wherein said number of saidpartial data placed along said non-arranged direction is less than orequal to (2^(m)−1)/4.
 5. Method of claim 2, wherein both of saidintegers s and t are zero.
 6. Method of claim 2, wherein both of saidintegers s and t are one.
 7. Method of claim 2, wherein said first setof parity information includes a plurality of said sums obtained foreach column using mutually different values of said integer s; and saidsecond set of parity information includes a plurality of said sumsobtained for each row using mutually different values of said integer t.8. Method of claim 1, wherein said partial data is said numerical dataobtained by expressing each of said biological compounds as data havinga size less than or equal to six bits.
 9. Method of claim 1, whereinsaid integer m that defines said Galois field GF(2^(m)) is a multiple of64.
 10. Method of claim 1, further comprising the steps of: making anassumption that said sequence of said biological compounds is a standardsequence; computing two sets of parity information on a sequence ofbiological compounds subject to examination, said two sets of parityinformation on said sequence of biological compounds subject toexamination corresponding to said two sets of parity information on saidstandard sequence; and identifying differences between said standardsequence and said sequence of biological compounds subject toexaminations by using said two sets of parity information on saidstandard sequence and said two sets of parity information on saidsequence of biological compounds subject to examination.
 11. Method ofclaim 1, wherein said biological compounds are nucleotides constitutingat least part of DNA, RNA, or a gene.
 12. Method of claim 1, whereinsaid biological compounds are amino acids constituting at least part ofa protein.
 13. Device for recording sequence information on biologicalcompounds, comprising: a sequencer for reading sequence information onsaid biological compounds; dividing means for dividing one of text datarepresenting a sequence of said biological compounds and numerical dataobtained by converting said text data utilizing a conversion rules intoa plurality of m-bit partial data arranged in a plurality of columns inan arranged direction corresponding to a direction along which saidbiological compounds are placed and in a plurality of rows in anon-arranged direction which crosses said arranged direction, where m isan integer greater than or equal to 16; computing means for computing afirst set of parity information by applying a first operation of aGalois field GF(2^(m)) along said non-arranged direction to a set ofsaid partial data of each column and computing a second set of parityinformation by applying a second operation of a Galois field GF(2^(m))along said arranged direction to a set of said partial data of each row;and recording means for recording said first and second sets of parityinformation in a recording medium.
 14. Device of claim 13, wherein whenα is a primitive element of a Galois field GF(2^(m)), said first set ofparity information includes a sum of a plurality of products obtained bymultiplying a set of said partial data of each column along saidnon-arranged direction by α^(sp), α^(s(p+1)), α^(s(p+2)), . . . ,α^(s(p+dp)), where s and p are nonnegative integers and dp is an integergreater than or equal to one; and said second set of parity informationincludes a sum of a plurality of products obtained by multiplying a setof said partial data of each row along said arranged direction byα^(tq), α^(t(q+1)), α^(t(q+2)), . . . , α^(t(q+dq)), where t and q arenonnegative integers and dq is an integer greater than or equal to one.15. Computer-readable medium for storing sequence information onbiological compounds, comprising: a data structure stored in saidmedium, wherein one of text data representing a sequence of saidbiological compounds and numerical data obtained by converting said textdata utilizing a conversion rule is divided into a plurality of m-bitpartial data arranged in a plurality of columns in an arrangeddirection, corresponding to a direction along which said biologicalcompounds are placed, and in a plurality of rows in a non-arrangeddirection which crosses said arranged direction, where m is an integergreater than or equal to 16; a first set of parity information iscomputed by applying a first operation of a Galois field GF(2^(m)) alongsaid non-arranged direction to a set of said partial data of each columnand a second set of parity information is computed by applying a secondoperation of a Galois field GF(2^(m)) along said arranged direction to aset of said partial data of each row; and said first and second sets ofparity information are recorded in said data structure as said sequenceinformation on said biological compounds.
 16. Computer-readable mediumof claim 15, wherein said data structure further includes a mathematicaldigest of one of said text data representing said sequence of saidbiological compounds and said numerical data corresponding to said textdata, and said mathematical digest larger has a size greater than orequal to 40 bits.
 17. Method for supplying sequence information onbiological compounds, comprising the steps of: recording one of textdata representing a sequence of said biological compounds and numericaldata obtained by converting said text data utilizing a conversion rule,in a first file; dividing said one of text data and numerical datarecorded in said first file into a plurality of m-bit partial dataarranged in a plurality of columns in an arranged directioncorresponding to a direction along which said biological compounds areplaced, and in a plurality of rows in a non-arranged direction whichcrosses said arranged direction, where m is an integer greater than orequal to 16; computing a first set of parity information by applying afirst operation of a Galois field GF(2^(m)) along said non-arrangeddirection to a set of said partial data of each column and computing asecond set of parity information by applying a second operation of aGalois field GF(2^(m)) along said arranged direction to a set of saidpartial data of each row; recording said first and second sets of parityinformation in a second file; and providing said two sets of parityinformation recorded in said second file through a communicationsnetwork.
 18. Method for utilizing sequence information on biologicalcompounds, comprising the steps of: receiving through saidcommunications network from a supplier said two sets of parityinformation recorded on said second file, according to claims 17;identifying differences between said sequence of said biologicalcompounds held by said supplier and a sequence of biological compoundssubject to examination, based on said two sets of received parityinformation; and when said differences cannot be recovered, receivingsequence information on a part corresponding to said differences, withinsaid one of text data and numerical data recorded in said first file,through said communications network from said supplier.
 19. Method ofclaim 18, wherein when α is a primitive element of a Galois fieldGF(2^(m)), said first set of parity information includes a sum of aplurality of products obtained by multiplying a set of said partial dataof each column along said non-arranged direction by α^(sp), α^(s(p+1)),α^(s(p+2)), . . . , α^(s(p+dp)), where s and p are nonnegative integersand dp is an integer greater than or equal to one; and said second setof parity information includes a sum of a plurality of products obtainedby multiplying a set of said partial data of each row along saidarranged direction by α^(tq), α^(t(q+1)), α^(t(q+2)), . . . ,α^(t(q+dq)), where t and q are nonnegative integers and dq is an integergreater than or equal to one.
 20. Method of claim 17, further comprisingthe step of: providing information on a number of said sequence of saidbiological compounds, and information on a mathematical digest of saidone of text data and numerical data through said communications network,21. Method for recording sequence information on biological compounds,comprising the steps of: dividing one of text data representing asequence of said biological compounds and numerical data obtained byconverting said text data utilizing a conversion rule, into a pluralityof m-bit partial data arranged in a plurality of columns in an arrangeddirection corresponding to a direction along which said biologicalcompounds are placed, and in a plurality of rows in a non-arrangeddirection which crosses said arranged direction, where m is an integergreater than or equal to 16; making assumptions that a maximum value ofsaid partial data is Nmax, and a prime number larger than said maximumvalue Nmax is P; computing a first set of parity information by applyinga first operation of a Galois field GF(P) along said non-arrangeddirection to a set of said partial data of each column; computing asecond set of parity information by applying a second operation of aGalois field GF(P) along said arranged direction to a set of saidpartial data of each row; and representing said sequence information onsaid biological compounds by said first and second sets of parityinformation.
 22. Method of claim 21, wherein said maximum value Nmax ofsaid partial data is smaller than (2^(m)−1) and said prime number Psatisfies the following condition:2^(m)>P>Nmax.
 23. Method of claim 22, wherein when δ is a primitiveelement of a Galois field GF(P), said first set of parity informationincludes a sum of a plurality of products obtained by multiplying a setof said partial data of each column along said non-arranged direction byδ^(sp), δ^(s(p+1)), δ^(s(p+2)), . . . , δ^(s(p+dp)), where s and p arenonnegative integers and dp is an integer greater than or equal to one;and said second set of parity information includes a sum of a pluralityof products obtained by multiplying a set of said partial data of eachrow along said arranged direction by δ^(tq), δ^(t(q+1)), δ^(t(q+2)), . .. , δ^(t(q+dp)), where t and q are nonnegative integers and dq is aninteger greater than or equal to one.
 24. Method for supplying sequenceinformation on biological compounds, comprising the steps of: recordingone of text data representing the sequence of said biological compoundsthe and numerical data obtained by converting said text data utilizing aconversion rules in a first file; dividing said one of said text dataand said numerical data recorded in said first file into a plurality ofm-bit partial data arranged in a plurality of columns in an arrangeddirection corresponding to a direction along which said biologicalcompounds are placed, and in a plurality of rows in a non-arrangeddirection which crosses said arranged direction, where m is an integerlarger than or equal to 16; making assumptions that a maximum value ofsaid partial data is Nmax, and a prime number larger than said maximumvalue Nmax is P; computing a first set of parity information by applyinga first operation of a Galois field GF(P) along said non-arrangeddirection to a set of said partial data of each column and computing asecond set of parity information by applying a second operation of aGalois field GF(P) along said arranged direction to a set of saidpartial data of each row; recording said first and second sets of parityinformation in a second file; and providing said two sets of parityinformation recorded in said second file through a communicationsnetwork.
 25. Method for utilizing sequence information on biologicalcompounds comprising the steps of: receiving through said communicationsnetwork from a supplier said two sets of parity information recorded insaid second file, according to claim 24; identifying differences betweensaid sequence of said biological compounds held by said supplier and asequence of biological compounds subject to examinations based on saidtwo sets of received parity information and when said differences cannotbe recovered, receiving sequence information on a part corresponding tosaid differences, within said one of text data recorded in said firstfile, through said communications network from said supplier
 26. Methodof claim 18, further comprising the step of: accessing at least one ofinformation on a number of said sequence of said biological compounds,and information on a mathematical digest of said one of text data andnumerical data, through said communications network.